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Programming Enigma Puzzles

2 August 2019

Posted by on **From New Scientist #2154, 3rd October 1998** [link]

To celebrate next week’s 1000th edition of

Enigma, we each made up an Enigma. Each one consisted of four clues leading to its own unique positive whole number answer. In each case none of the four clues was redundant. To avoid duplication, Keith made up his Enigma first and showed it to Susan before she made up hers.The two Enigmas were meant to be printed side-by-side but the publishers have made a (rare) error and printed the clues in a string:

(A) It is a three-figure number;

(B) It is less than a thousand;

(C) It is a perfect square;

(D) It is a perfect cube;

(E) It has no repeated digits;

(F) The sum of its digits is a perfect square;

(G) The sum of its digits is a perfect cube;

(H) The sum of all the digits which are odd in Keith’s answer is the same as the sum of all the digits which are odd in Susan’s.Which four clues should have formed Keith’s Enigma, and what was the answer to Susan’s?

There are now 1300 *Enigma* puzzles available on the site (or at least 1300 posts in the *enigma* category). There are 492 *Enigma* puzzles remaining to post.

There are currently also 76 puzzles from the *Tantalizer* series, 75 from the *Puzzle* series and 13 from the new *Puzzle #* series of puzzles that have been published in *New Scientist* which together cover puzzles from 1975 to 2019 (albeit with some gaps).

I also notice that the **enigma.py** library is now 10 years old (according to the header in the file – the creation date given coincides with me buying a book on *Python*). In those 10 years it has grown considerably, in both functionality and size. I’m considering doing a few articles focussed on specific functionality that is available in the library.

[enigma999]

12 July 2019

Posted by on **From New Scientist #2157, 24th October 1998** [link]

Albion have been playing in Europe, where the result of any fixture is decided by the aggregate scores achieved by the teams on two matches, each team being at home for one match and away for the other match. If the aggregate scores over the two matches are equal the rule is that the team that has scored more goals away from home wins.

Albion played in and won five fixtures in Europe. In four of them the aggregate scores were equal and Albion won each time on the “away goals” rule, even though in their five away matches Albion scored fewer goals than in their five home matches.

No two matches out of the ten that Albion played had the same score and no team scored more than three goals in any of the matches.

What were the scores in Albion’s five home matches? Give each score in the form

x-y, with Albion’s score first in each match.

I was going to mention that there are now “only” 500 *Enigma* puzzles left to post, but when I counted it up it looked like there were “only” 498 left, so I should have mentioned this with **Enigma 1003**. Although it is hard to be exact (there are duplicate puzzles, corrections, and sometimes extra puzzles at Christmas) I think it is safe to say that there are about 1294 *Enigma* puzzles posted so far, and about 498 left, so we are about 72% of our way through the *Enigma* puzzles.

[enigma1002]

3 May 2019

Posted by on **From New Scientist #2168, 9th January 1999** [link]

In this sum each letter represents a different digit. The same letter represents the same digit wherever it appears and no number starts with a zero.

What is the 5-digit number represented by EIGHT?

This is the first puzzle that was published in 1999, so there is now a complete 15 year archive of *Enigma* puzzles from the start of 1999 to the final *Enigma* puzzle published in December 2013. There is also a complete 11 year archive of earlier puzzles from October 1977 to January 1989. As well as *Tantalizer* puzzles from 1976 and 1977. This brings the total number of archived puzzles to over 1400. I will continue to expand the archive by posting puzzles on a regular schedule.

[enigma1012]

1 May 2019

Posted by on **From New Scientist #981, 1st January 1976** [link]

To shake down the plum pud, the five adults held three post-prandial athletic events. Each competitor scored the number of the place gained in each event, with the aim of totalling as few points as possible overall. Thus Uncle Arthur came second in the hop and scored 2 points for it. There were no ties in any event or in the overall totals and no one took the same place in two or more events.

Aunt Barbara, although bottom in one event, was top at skipping, Mother having been forced down to third place by a fit of hiccoughs. Father did better than Uncle Charlie at hopping. Uncle Arthur did not win the jumping. Mother did better at jumping than at hopping. Aunt Barbara was not second overall. The overall winner did not win the hopping.

As your post-prandial exercise, would you care to list the order in each event?

The puzzle can be solved as presented, but has two solutions. To arrive at the published single solution we seem to need an extra fact — *“Uncle Arthur finished in third place overall”*.

This puzzle completes the archive of *Tantalizer* puzzles from 1976. There is a full archive from this puzzle to the final *Tantalizer* puzzle in May 1977 (when the *Puzzle* series started).

[tantalizer430]

1 April 2019

Posted by on **From New Scientist #1644, 24th December 1988** [link]

The five couples in Yuletide Close send cards to some of their neighbours. Some of them told me who (apart from themselves) send cards.

Alan:“The cards not involving us are the ones exchanged between Brian’s and Charles’s houses, the ones exchanged between Brian’s and Derek’s, the card from Charles to Derek (or the other way round, I’m not sure which) and the card from Brian to Eric (or the other way round).”

Brenda:“Apart from our cards, Alice and Emma exchange cards, as do Dawn and Christine, and Dawn sends Emma one.”

The Smiths:“The cards not involving us are the ones exchanged by the Thomases and the Unwins, those exchanged by the Williamses and the Vincents, the one from the Thomases to the Williamses and one between the Unwins and the Vincents (but I forget which way).”

No 3:“Nos 1 and 5 exchange cards, one card passes between Nos 2 and 4 (I don’t know which way) and No 2 sends one to No 1.”Charles Thomas receives the same number of cards as he sends. On Christmas Eve, he goes on a round tour for drinks. He delivers one of his cards, has a drink there, takes one of their cards and delivers it, has a drink there, takes one of their cards and delivers it, has a drink there, takes one of their cards and delivers it, has a drink there, collects the card from them to him and returns home, having visited every house in the close.

Name the couples at 1-5 (for example: 1, Alan and Brenda Smith; 2, …).

**Enigma 1321** is also called “Christmas cards”.

This completes the archive of *Enigma* puzzles from 1988. There is now a complete archive from the start of *Enigma* in 1979 to the end of 1988, and also from February 1999 to the final *Enigma* puzzle at the end of 2013. There are 1265 *Enigma* puzzles posted to the site, which is around 70.8% of all *Enigma* puzzles published.

[enigma493b] [enigma493]

1 January 2019

Posted by on There are now 1,239 *Enigma* puzzles on the site, along with 61 from the *Tantalizer* series and 60 from the *Puzzle* series (and a few other puzzles that have caught my eye). There is a complete archive of *Enigma* puzzles published between January 1979 to September 1988, and from May 1999 up to the final *Enigma* puzzle in December 2013, which make up about 69.3% of all the *Enigma* puzzles published. Of the remaining 553 puzzles I have 125 left to source (numbers 900 – 1024).

In 2018, 105 *Enigma* puzzles were added to the site (and 26 *Tantalizers,* 26 *Puzzles*, and 3 others, so 160 puzzles in total).

Here is my selection of the puzzles that I found most interesting to solve over the year:

**Enigma 432: Holiday on the islands****Enigma 442a: Hark the herald angels sing****Enigma 460: Tear me off a strip****Enigma 476: A curious question****Enigma 479: Road island**

::

**Enigma 1072: Into three piles****Enigma 1069: Time for elevenses****Enigma 1066: Members of the clubs****Enigma 1064: Low score draw****Enigma 1060: In order to solve…****Enigma 1057: Recycled change****Enigma 1041: Lucky sixes****Enigma 1037: The perfect shuffle****Enigma 1035: Connected numbers**

::

**Puzzle 52: Football on the Island of Imperfection****Tantalizer 448: Love and hate****Tantalizer 447: Marching order****Grid puzzle****Sunday Times Teaser 2503****Sunday Times Teaser 2907: Combinatorial cards**

::

Thanks to everyone who has contributed to the site in 2018, either by adding their own solutions (programmatic or analytical), insights or questions, or by helping me source puzzles from back-issues of *New Scientist*.

20 August 2018

Posted by on **From New Scientist #2204, 18th September 1999** [link]

A square field has its sides running north-south and east-west. The field is divided into an 8 × 8 array of plots. Some of the plots contain cauliflower. A line of plots running west to east is called a row and line of plots running north to south is called a column.

John selects a row and walks along it from west to east, writing down the content of each plot as he passes it; he writes E to denote an empty plot and C to denote a plot containing cauliflower; he writes down EECECCEC. He repeats this for the other seven rows and writes down ECEECCCE, ECECEECC, ECCECCEE, CEECEECC, CECECECE, CECCECEE and CCECEEEC. The order in which John visits the rows is not necessarily the order in which they occur in the field.

Similarly, Mark selects a column and walks along it from north to south, writing down the content of each plot as he passes it; he writes down EECECCCE. He repeats this for the other seven columns and writes down EECCEECC, ECECECEC, ECCECEEC, CEECCECE, CECECECE, CCEEECEC and CCECECEE. The order in which Mark visits the columns is not necessarily the order in which the occur in the field.

Draw a map of the field, showing which plots contain a cauliflower.

**Enigma 1248** was also called **“Rows and columns”**.

There are now 1200 *Enigma* puzzles on the site (although there is the odd repeated puzzle, and at least one puzzle published was impossible and a revised version was published as a later *Enigma*, but the easiest way to count the puzzles is by the number of posts in the “*enigma*” category).

There is a full archive of *Enigma* puzzles from **Enigma 1** (February 1979) to **Enigma 461** (May 1988), and of the more recent puzzles from **Enigma 1048** (September 1999) up to the final *Enigma* puzzle, **Enigma 1780** (December 2013). Which means there are around 591 *Enigma* puzzles to go.

Also on the site there are currently 53 puzzles from the *Tantalizer* series, and 50 from the *Puzzle* series, that were published in **New Scientist** before the *Enigma* series started.

Happy Puzzling!

[enigma1048]

20 July 2018

Posted by on **From New Scientist #1608, 14th April 1988** [link]

In the following division sum, letters are substituted for digits. The same letter stands for the same digit wherever it appears, and different letters stand for different digits.

Rewrite the sum with letters replaced by digits.

This puzzle brings the total number of *Enigma* puzzles on the site to 1192, which means there are now more than 2/3 of all *Enigma* puzzles published in *New Scientist* on the site. There is a full archive of puzzles from October 1999 to the final *Enigma* puzzle in December 2013 (728 puzzles), and also a full archive from the first *Enigma* puzzle in February 1979 up to this puzzle from April 1988 (462 puzzles — there were sometimes multiple puzzles at Christmas). This leaves around 600 puzzles to be posted. Thanks to the ongoing efforts of Hugh Casement I have been able to acquire the text for most of these remaining puzzles (I have 134 left to source), so I can continue to keep posting them. There are also 48 puzzles on the site from the *Puzzle* sequence (with 43 left to go), and 51 puzzles from the *Tantalizer* sequence (I think I will be able to source around 268 more of these). Happy Puzzling!

[enigma457]

30 April 2018

Posted by on **From New Scientist #2220, 8th January 2000** [link]

You play this game by first drawing 20 boxes in a continuous row. You then draw a star in each box in turn, in any order. Each time you draw a star you earn a score equal to the number of stars in the unbroken row [of stars] that includes the one you have just drawn.

Imagine that you have already drawn eleven stars as shown below, and you are deciding where to place the twelfth.

Drawing the next star in box 1 would score only 1 point, in box 11 it would score 2 points. A star in box 2, 5 or 6 would score 3 points, and in box 9, 12 or 19 it would score 4 points. Drawing the star in box 16 would score 6 points.

Your objective is to amass the lowest possible total for the 20 scores earned by drawing the 20 stars.

What is that minimum total?

This puzzle completes the archive of *Enigma* puzzles from 2000. There are now 1169 *Enigma* puzzles available on the site. There is a complete archive from the beginning of 2000 until the end of *Enigma* in December 2013 (14 years), and also from the start of *Enigma* in February 1979 up to January 1988 (10 years), making 24 years worth of puzzles in total. There are 623 *Enigma* puzzles remaining to post (from February 1988 to December 1999 – just under 11 years worth), so I’m about 62% of the way through the entire collection.

[enigma1064]

6 April 2018

Posted by on **From New Scientist #1592, 24th December 1987** [link]

After our successful pantomime production in which I played the leading lady, I gave my little costarring helpers some gifts from a big bag of different trinkets, and they each got a different number and none were left.

To make it fairer I gave each helper 10p for each gift that he

didn’tget and deducted 40p for each gift that hedidget, but that still gave each of them some 10p coins as well as some gifts. It cost me £12.60 in addition to the gifts.What was the highest number of gifts received by any helper (that little fellow got less than 50p cash)?

What part was I playing?

This puzzle completes the archive of *Enigma* puzzles from 1987. There is now a complete archive from the start of *Enigma* in February 1979 to the end of 1987, and also from February 2000 to the final *Enigma* puzzle in December 2013. Making 1162 *Enigma* puzzles posted so far, which means there are about 626 left to post.

[enigma442b] [enigma442]

31 December 2017

Posted by on There are now 1,134 *Enigma* puzzles on the site, along with 35 from the *Tantalizer* series and 34 from the *Puzzle* series (and a few other puzzles that have caught my eye). There is a complete archive of *Enigma* puzzles published between January 1979 to September 1987, and from May 2000 up to the final *Enigma* puzzle in December 2013, which make up about 63.3% of all the *Enigma* puzzles published. Of the remaining 654 puzzles I have 152 left to source (numbers 891 – 1042).

In 2017, 105 *Enigma* puzzles were added to the site (and 30 *Tantalizers* and 28 *Puzzles*, so 163 puzzles in total). Here is my selection of the puzzles that I found most interesting to solve over the year:

**Enigma 381: Island airlines****Enigma 382: Dice****Enigma 383: Stop watch****Enigma 391b: Christmas recounted****Enigma 409: Hands and feet****Enigma 413: Quargerly dues****Enigma 415: Buses galore****Enigma 426: Time and again****Enigma 429: Professor Quark**

::

**Enigma 1134: Luck be a lady****Enigma 1132: Phone back****Enigma 1127: Lights out**(see also:**Enigma 1137**)**Enigma 1126: Enigmatic dice****Enigma 1124: Classy glass****Enigma 1112: Patio zones****Enigma 1110: Dots and lines****Enigma 1101: Disappearing numbers****Enigma 1097: Chessboard triangles****Enigma 1091: One’s best years****Enigma 1087: Egyptian triangles****Enigma 1085: Cut and run****Enigma 1084: 1-2-3 triangles****Enigma 1082: End-of-season blues**

::

**Tantalizer 490: Diplomatic niceties****Tantalizer 484: Blockwork****Tantalizer 474: Desert crossing****Puzzle 82: A cross number**

::

I have continued to maintain the **enigma.py** library of useful routines for puzzle solving. In particular the `SubstitutedExpression()` solver and `Primes()` class have increased functionality, and I have added the ability to execute *run files*, in cases where a complete program is not required. The `SubstitutedDivision()` solver is now derived directly from the `SubstitutedExpression()` solver, and is generally faster and more functional than the previous implementation.

I’ve also starting putting my **Python** solutions up on **repl.it**, where you can execute the code without having to install a Python environment, and you can make changes to my code or write your own programs (but a free login is required if you want to save them).

Thanks to everyone who has contributed to the site in 2017, either by adding their own solutions (programmatic or analytical), insights or questions, or by helping me source puzzles from back-issues of *New Scientist*.

1 September 2017

Posted by on **From New Scientist #1562, 28th May 1987** [link]

Professor Kugelbaum, deep in thought and in a distracted state, wandered onto a building site. He saw a man laying equilateral triangular slabs on a plain flat area. Turning his keen mind from the abstract to the concrete, he asked the man with a sudden inspiration, “What are you doing?”

“I’m laying a town square.”

“But the angles aren’t right.”

“Well, it’s going to be a square in the form of an enormous equilateral triangle”, was the reply.

“I don’t call nine slabs enormous.”

“Ah”, said the workman, “first, I haven’t finished yet: I’ve just started at one apex. Secondly, if you look carefully, you’ll see that there are in fact 13 different triangles to be found in the pattern I’ve already laid [see diagram]. When I’ve finished there will be 6000 times as many

moretriangles to be found in the completed array.”Kugelbaum’s mind began to tick over.

How many slabs will there be in the completed array?

This puzzle brings the total number of *Enigma* puzzles on the site to 1,100 (and by a curious co-incidence on Monday I posted **Enigma 1100** to the site). This means there are (only!) 692 *Enigma* puzzles remaining to post, mostly from the 1990s. There is a full archive of puzzles from the inception of *Enigma* in February 1979 up to May 1987 (this puzzle), and also from September 2000 up to the end of *Enigma* in December 2013. Happy puzzling!

[enigma412]

8 May 2017

Posted by on **From New Scientist #2272, 6th January 2001** [link]

Albion, Borough, City, Rangers and United played a tournament in which each team played each of the other teams once. Two matches took place in each of five weeks, each team having one week without a match.

One point was awarded for winning in the first week, 2 points for winning in the second week, 3 points for winning in the third week, 4 points for winning in the fourth week and 5 points for winning in the fifth week. For a drawn match each team gained half the points it would have gained for winning it. At any stage, teams that had gained the same number of points were regarded as tying.

After the first week A led, with B tying for second place. After the second week B led, with C tying for second place. After the third week C led, with R tying for second place. After the fourth week R led, with U tying for second place. After the fifth week U had won the tournament with more points than any of the other teams.

(1) Which team or teams finished in second place after the fifth week?

(2) Give the results of Albion’s matches, listing them in the order in which they were played and naming the opponents in each match.

This completes the archive of *Enigma* puzzles from 2001. There are now 1065 *Enigma* puzzles on the site, the archive is complete from the beginning of *Enigma* in February 1979 to January 1987, and from January 2001 to the final *Enigma* puzzle in December 2013. Altogether there are currently 59.5% of all *Enigmas* published available on the site, which leaves 726 *Enigmas* between 1987 and 2000 left to publish.

[enigma1116]

14 April 2017

Posted by on **From New Scientist #1540, 25th December 1986** [link]

Delivering Christmas presents is not an easy task and Exe-on-Wye has grown to be so populous that it is hardly surprising that this year Santa Claus decided to delegate the delivery to his minions. Thanks to some failure in communication, however, instead of each house receiving one sack of presents, each of his helpers left a sack at each and every house. The number of sacks that should have been delivered happens to be the number obtained by striking out the first digit of the number of sacks delivered.

When Santa Claus discovered this, he was not pleased. “Things couldn’t be worse!” he groaned. “The number of sacks you should have delivered is the largest number not ending in zero to which the addition of a single digit at the beginning produces a multiple of that number”. And he disciplined the unhappy helpers.

But for each unhappy helper there were many happy households in Exe-on-Wye on Christmas morning.

Can you say how many unhappy helpers and how many happy households?

This puzzle completes the archive of *Enigma* puzzles from 1986, and brings the total number of *Enigma* puzzles on the site to 1,058. There is a complete archive from the start of *Enigma* in February 1979 to the end of 1986, as well as a complete archive from February 2001 to the end of *Enigma* in December 2013, which is 59% of all *Enigma* puzzles, and leaves 733 *Enigma* puzzles left to publish.

I have also started to post the *Tantalizer* and *Puzzle* problems that were precursors to the *Enigma* puzzles in **New Scientist**, and so far I have posted 16 of each. In total there are 90 *Puzzles* (which I can get from *Google Books*) and 500 *Tantalizer* puzzles (of which the final 320 are available in *Google Books*).

Happy puzzling (and coding)!

[enigma391b] [enigma391]

31 December 2016

Posted by on There are now 1,028 *Enigma* puzzles on the site (plus a few other puzzles). There is a complete archive of all puzzle published from January 1979 to September 1986 and also from May 2001 to December 2013, which is about 57.5% of all *Enigma* puzzle published in *New Scientist* and leaves around 760 puzzles to add to the site.

In 2016 I added 105 *Enigma* puzzles to the site (as well as a puzzles from other sources). Here’s my selection of the ones I found most interesting to solve this year:

**Enigma 329: Clear short circuit****Enigma 343: In the mews****Enigma 344: Five-nations championship****Enigma 359: Neat odd quad****Enigma 362: On the face of it****Enigma 373: Date the painting**

**Enigma 1182: Recurring decimals****Enigma 1174: Small sums****Enigma 1172: Plant a tree****Enigma 1154: Funny money****Enigma 1152: Tet on the Nile****Enigma 1147: Multiply and add****Enigma 1146: Units fore and aft****Enigma 1143: Count and count****Enigma 1137: On, off, on, off**

I have continued to maintain the **enigma.py** library (in particular I added some routines to help in solving football problems with letters substituted for digits in score tables, and for solving general *Alphametic* problems). I wrote up some notes on the solving of *Alphametics* using *Python* here and here, and the `SubstitutedExpression()` class in **enigma.py** can now be used to solve many *Enigma* problems directly.

Since switching to posting puzzles on Monday and Friday I have also added Wednesday *Bonus* Puzzles, which are posted on Wednesdays (naturally), if I have the time. Unless there is a particularly interesting puzzle that’s caught my eye that week I will alternate posting *Tantalizer* (set by Martin Hollis) and *Puzzle* (set by Eric Emmet) problems, which are the predecessors of the *Enigma* puzzles in **New Scientist**. (Although Eric Emmet seems to like puzzles involving substituted addition or division sums, and football problems a bit too much for my liking).

Thanks to everyone who has contributed to the site in 2016, either by adding their own solutions (programmatic or analytical), insights or questions, or by helping me source puzzles from back-issues of *New Scientist*.

30 September 2016

Posted by on **From New Scientist #1513, 19th June 1986** [link]

“We Yorkshireman,” said my friend Triptolemus, “like a puzzle as a cure for insomnia, instead of counting sheep. Have you got a nice simple question, without a mass of figures to remember?”

So I said, “If a wrong-angled triangle has whole-number sides and an area equal to its perimeter, how long are its sides?”

He slept on the the problem and gave me the answer next morning.

Can you?

(A wrong-angled triangle is of course the opposite of a right-angled triangle. Instead of two of its angles adding up to 90°, it has two angles

differingby 90°).

There are now 1000 *Enigma* puzzles on the site, with a full archive of puzzles from **Enigma 1** (February 1979) up to this puzzle, **Enigma 364** (June 1986) and also all puzzles from **Enigma 1148** (August 2001) up to the final puzzle **Enigma 1780** (December 2013). Altogether that is about 56% of all the *Enigma* puzzles ever published.

I have been able to get hold of most of the remaining puzzles up to the end of 1989 and from 2000 onwards, so I’m missing sources for most of the puzzles originally published in from 1990 to 1999. Any help in sourcing these is appreciated.

[enigma364]

31 December 2015

Posted by on There are now 923 *Enigma* puzzles on the site. There is a complete archive of all puzzles published from January 1979 – September 1985 and also from May 2002 – December 2013. Which is about 52% of all *Enigma* puzzles published in *New Scientist*, and leaves around 860 puzzles to add to the site.

In 2015 I added 160 *Enigma* puzzles (as well as a handful of puzzles from other sources). Here’s my selection of the ones I found most interesting to solve programatically this year:

**Enigma 252: Three-point circle****Enigma 257: Hexa-draughts****Enigma 258: Monkey business****Enigma 266: Twelve trees****Enigma 278: Uncle Pinkle’s new system****Enigma 287: GAGA’s friends****Enigma 288a: Multiplets****Enigma 288b: Christmas viewing****Enigma 289: All for one****Enigma 293: Red is not a colour****Enigma 295: The max-multiple game****Enigma 321: Going to pieces****Enigma 325: Clear thin circuit**

**Enigma 1190: Triple duel****Enigma 1194: Only two coins****Enigma 1221: Flower beds****Enigma 1225: Rows are columns****Enigma 1226: Megafactors****Enigma 1240: Stack ’em high****Enigma 1241: Jigsaw squares****Enigma 1244: All in one****Enigma 1247: Recurring decimal****Enigma 1248: Rows and columns****Enigma 1249: Root routes****Enigma 1251: Jigsaw of rectangles****Enigma 1252: Cards on the table****Enigma 1253: Votes and taxes****Enigma 1254: Piles of money****Enigma 1260: Latin fives**

During 2015 I switched to posting puzzles twice a week (on Monday and Friday, with the occasional extra posting on Wednesdays if I had something interesting to post), so there are around 8 years worth of puzzles to go.

Thanks to everyone who has contributed to the site in 2015, either by adding their own solutions (programmatic or analytical), insights or questions, or by helping me source puzzles from back-issues of *New Scientist*.

Here is the **2015 Annual Report** for *Enigmatic Code* generate by **WordPress**.

4 December 2015

Posted by on **From New Scientist #1470, 22nd August 1985** [link]

The new method of rewarding goals scored in football matches is a great success. And some people say that the goals have increased not only in quantity but also in quality.

In this method 10 points are awarded for a win, 5 points for a draw and 1 point for each goal scored.

In a recent competition between 4 teams (

A,B,CandD),Agot 5 points,Bgot 35 points,Cgot 20 points, andDgot 4 points, after some — or perhaps all — of the matches were played.Not more than 10 goals were scored in any match and that number was only scored in one. Each side scored at least 1 goal in every game.

What was the score in each match?

It’s now 4 years since I started the *Enigmatic Code* site, and we have 916 **Enigma** puzzles on the site, which is just over half the total number of *Enigma* puzzles published in *New Scientist* between 1979 and 2013. There is a complete archive from the very first *Enigma* puzzle in January 1979 up to August 1985, and from June 2002 to the final *Enigma* puzzle in December 2013.

I aim to keep adding puzzles as long as I am able to source them. I currently need to get puzzles from #545 (January 1990) to #1154 (October 2001), along with #1166 (22nd? December 2001), #1176 (2nd March 2002), #1181 (6th April 2002) and #1186 (11th May 2002), (altogether around 600 puzzles), so I shall have to try and get to a reference library to get access to back issues of the magazine.

Thank you to everyone who has joined in by sharing their own solutions and insights.

[enigma322]

9 October 2015

Posted by on **From New Scientist #1462, 27th June 1985** [link]

In the following football table and addition sum, letters have been substituted for digits (from 0 to 9). The same letter stands for the same digit wherever it appears, and different letters stand for different digits.

(1) The four teams are eventually going to play each other once, or perhaps they have already done so. With one exception, all the matches were won by a margin of only one goal.

(Two points are given for a win and one point to each side in a drawn match).

(2)

Find the scores in the football matches, and write out the addition sum with numbers substituted for letters.

This is the 900th **Enigma** puzzle to be posted to the site. The archive currently contains *Enigmas* 1 – 314 (Feb 1979 – Jun 1985) and *Enigmas* 1199 – 1780 (Aug 2002 – Dec 2013).

[enigma314]

18 September 2015

Posted by on **From New Scientist #1459, 6th June 1985** [link]

The ages of George’s four daughters add up to 70. Amanda says that the exact figures are 8, 16, 21, and 25. But Brenda says that Celia is 15. Delia, on the other hand, says that Celia is 18.

This is all very confusing, until you know about a strange family habit. It is to state one’s own age correctly but to overstate the age of anyone older and to understate the age of anyone younger.

Even after making all possible deductions so far, you cannot work out the age of each daughter. For that you need a bit more information, for instance the number of years separating Belinda and Celia.

Please supply the name and age of the four.

There are now 894 **Enigma** puzzles on the site, and I think this is around half of all the **Enigma** puzzles published in *New Scientist*, from **Enigma 1** in February 1979 to **Enigma 1780** in December 2013.

To help me keep on top of posting the remaining **Enigma** puzzles I’m going to change the posting schedule to two puzzles a week, one on Friday and one on Monday. Which means, if I can keep sourcing the puzzles, I will have enough to last another 8.6 years!

[enigma311]

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