Enigmatic Code

Programming Enigma Puzzles

Category Archives: site news

Intermission

I won’t be able to add new puzzles or comments to the site for the next few days.

Hopefully normal service will be resumed shortly.

2019 in review

Happy New Year from Enigmatic Code!

There are now 1343 Enigma puzzles on the site, along with 86 from the Tantalizer series and 85 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 1989, and from May 1998 up to the final Enigma puzzle in December 2013, which make up just over 75% of all the Enigma puzzles published. Of the remaining 450 puzzles I have 75 left to source (numbers 901 – 976).

In 2019, 103 Enigma puzzles were added to the site (and 25 Tantalizers, 25 Puzzles, and 40 others, so 193 puzzles in total).

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

Older Puzzles (from 1988 – 1989)

::

Newer Puzzles (from 1998 – 1999)

::

Other Puzzles

::

Sunday Times Teasers

I have also been collecting some old Teaser puzzles originally published in The Sunday Times on the S2T2 site, as well as accumulating my notes for more recent Teaser puzzles that I solved at the time. There are currently 232 puzzles available on the S2T2 site.

Here are some that I found interesting to solve (or revisit):

::

Between both sites I have posted 426 puzzles in total this year. I don’t expect to maintain this rate in the future.

Thanks to everyone who has contributed to the sites in 2019, either by adding their own solutions (programmatic or analytical), insights or questions, or by helping me source puzzles from back-issues of New Scientist.

Enigma 978: The ABC brick company

From New Scientist #2133, 9th May 1998

The ABC brick company prides itself on making unique toys. It has just produced a range of wooden bricks, all of the same size, in the shape of a tetrahedron (a solid with four equilateral-triangle faces). Each of the four faces on every tetrahedron is painted in one of the company’s standard colour range. For example, one of the bricks has one yellow face, two blue faces, and a green face. The company ensures that each tetrahedron is different — there is no way of rotating one to make it look like another. With that restriction in mind, the company has manufactured the largest possible number of these bricks.

To add to the uniqueness of the toys, each brick is placed in an individual cardboard box with the letters “ABC” stencilled on it. Then using the same standard range of the company’s colours, an artist paints each of the letters on the boxes. For example, one has a red “A”, a blue “B”, and a red “C”. No two of the colourings of the ABCs are the same, and, with that restriction in mind, once again the company has produced the largest possible number of boxes.

By coincidence, there are just enough boxes to put one of the tetrahedra in each.

How many colours are there in the company’s standard range?

News

There are now 450 Enigma puzzles remaining to post, which means that 75% of all Enigma puzzles are now available on the site.

[enigma978]

Enigma 528: An enigma for U

From New Scientist #1680, 2nd September 1989 [link]

Here are just three rows from our local football league table at the end of the season, after each team in the league has played each of the others once. The teams have been put in alphabetical order here.

Enigma 528

There are three points for a win and one for a draw and, in the table, digits have been consistently replaced by letters with different letters used for different digits.

Please find AGAIN. And tell me who (if anybody) won when City played Albion.

News

It’s the 8th anniversary of Enigmatic Code, and this puzzle brings the total number of Enigma puzzles posted to 1335, which is 75% of the 1780 Enigma puzzles published in New Scientist. There is a complete archive of puzzles from the first Enigma puzzle in February 1979 up to September 1989, and also from June 1998 up to the final Enigma puzzle in December 2013. There are 457 Enigma puzzles remaining to post.

Also available are puzzles from the Puzzle series, which were published in New Scientist before Enigma started. There is a complete archive available from July 1977 until the end of the Puzzle series in February 1979 (83 puzzles). There are 7 puzzles in this series remaining to post.

And before that was the Tantalizer series of puzzles, of which there is a complete archive from September 1975 up to the end of the Tantalizer series in May 1977 (84 puzzles).

Earlier in 2019 New Scientist started publishing a new series of puzzles (the “Puzzle #” series), and I have been posting these to the site, along with my notes, as they became available.

I have also been posting my notes on Sunday Times Teaser puzzles at the S2T2 site, and there are currently 227 puzzles available there.

So between the two sites there are currently 1766 puzzles available, which is almost the total number of Enigma puzzles published.

[enigma528]

Enigma 999: Combined celebrations

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?

News

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]

Enigma 1002: Albion in Europe

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.

News

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]

Enigma 1012: Pieces of eight

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?

News

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]

Tantalizer 430: Hop, skip and jump

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”.

News

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]

Enigma 493b: Christmas cards

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”.

News

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]

2018 in review

Happy New Year from Enigmatic Code!

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:

Older Puzzles (from 1987 – 1988)

::

Newer Puzzles (from 1999 – 2000)

::

Other Puzzles

::

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.

Enigma 1048: Rows and columns

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”.

News

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]

Enigma 457: Divided by ex…

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.

Enigma 457

Rewrite the sum with letters replaced by digits.

News

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]

Enigma 1064: Low score draw

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?

News

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]

Enigma 442b: Oh yes I did! Oh no you didn’t!

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’t get and deducted 40p for each gift that he did get, 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?

News

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]

2017 in review

Happy New Year from Enigmatic Code!

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:

Older Puzzles (from 1986 – 1987)

::

Newer Puzzles (from 2000 – 2001)

::

Other Puzzles

::

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.

Enigma 412: A triangular square

From New Scientist #1562, 28th May 1987 [link]

Enigma 412

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 more triangles to be found in the completed array.”

Kugelbaum’s mind began to tick over.

How many slabs will there be in the completed array?

News

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]

Enigma 1116: United win at last

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.

News

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]

Enigma 391b: Christmas recounted

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?

News

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]

2016 in review

Happy New Year from Enigmatic Code!

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:

Older Puzzles (1985 – 1986)

Newer Puzzles (2001 – 2002)

Other Puzzles

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.

Enigma 364: Wrong-angled triangle

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 differing by 90°).

News

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]

%d bloggers like this: