Enigmatic Code

Programming Enigma Puzzles

Category Archives: site news

Enigma 1064: Low score draw

From New Scientist #2220, 8th January 2000

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]

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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?

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 (1986 – 1987)

Newer Puzzles (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?

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.

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?

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°).

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]

2015 in review

Happy New Year from Enigmatic Code!

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:

Older puzzles (1984 – 1985)

Newer puzzles (2002 – 2003)

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.

Enigma 322: More and better goals

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 (ABC and D), A got 5 points, B got 35 points, C got 20 points, and D got 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]

Enigma 314: Football and addition

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.

Enigma 314 - A

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

(2)

Enigma 314 - B

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]

Enigma 311: Three score years and ten

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]

Enigma 309: Missing letters

From New Scientist #1457, 23rd May 1985 [link]

In the following division sum, some of the digits are missing and some are replaced by letters. The same letter stands for the same digit whenever it appears, and different letters stand for different digits.

Enigma 309

Find the correct sum.

This puzzle brings the total number of Enigma puzzles on the site to 890. Since the final puzzle was Enigma 1780 you might expect that we now have 50% of all Enigma puzzles ever published available in the archive. However since there are sometimes multiple puzzles published with the same number (typically at Christmas) I don’t think we’re quite there yet. But I’ll be marking the “half-way” milestone sometime next week.

[enigma309]

Enigma 1257: Boxing clever

From New Scientist #2413, 20th September 2003 [link]

Triangulo, the world-famous Cuban cubist, has created five boxes, each of which contains a number of cubes of the same colour, but with a different colour in each box.

At a master class, he tries to construct a particular size of cube using all the cubes from just two boxes.  But whichever pair he selects, he finds that at least one pair has too many pieces and all the other pairs have too few.

Each different pair of boxes gives a different total of cubes and the largest total is 10 more than the smallest.

With a stoke of genius, using all the cubes together, he creates instead a flat square, multi-coloured masterpiece!

How many cubes (in ascending order) are there in each box?

This puzzle is Enigma 1257 and the previous puzzle I published was Enigma 256, so there are now 1,000 puzzles left to publish (ignoring for the moment that sometimes multiple puzzles are published under the same number, and that I’ve already published Enigma 1095). Which means just under 44% of all Enigma puzzles are now available on the site.

[enigma1257]

Enigma 255: Two heads are better than one

From New Scientist #1402, 22nd March 1984 [link]

“Care for a flutter?” Alf asked Bert.

“Suits me,” Bert replied.

“We need a 50p, a 20p, a 10p and a 5p coin. I’ll contribute one of them and you the other three.”

“Then what?”

“We toss all four. If any come up Heads, then whichever of us has the most money (not the most coins) head-side up scoops all four coins. If all four come up Tails, we toss again.”

“OK. Who contributes what?”

“Well,” said Alf, “as I am putting in only one coin, I’ll decide which it is to be.”

Which coin gives the crafty Alf the best bet?

This puzzle brings the total number of Enigma puzzles on the site to 780. As the final Enigma was #1780, you might think that means there are 1,000 puzzles left to publish. But at Christmas time, especially in the 80’s, multiple puzzles were often published under the same number. (Also, I’ve so far come across three puzzles that are duplicates of already published puzzles). So, my current estimate is that I will need to publish around 1,788 puzzles to have a full archive of Enigma puzzles, so it’ll be a couple of weeks before there are around 1,000 puzzles left to go.

[enigma255]

2014 in review

Happy New Year from Enigmatic Code!

There are now 763 Enigma puzzles on the site. There is a complete archive of all puzzles published from 1979 – 1983 and also from 2004 – 2013. Which is about 43% of all Enigma puzzles, and leaves just over 1,000 to add to the site.

In 2014 I added 182 puzzles to the site – here my selection of the ones I found most interesting to solve programatically:

Older Puzzles (1982 – 1983)
Newer Puzzles (2003 – 2005)

Of course the most challenging problem of 2014, but certainly not the most fun, was getting a phone line and internet service at my new house. But I did manage to keep up with the posting schedule (although somewhat erratically) during the 3 months that I was without internet access.

Thank you to everyone who has contributed to the site by adding their own solutions (programmed or otherwise) or their insights and questions.

Here is the 2014 Annual Report for Enigmatic Code created by WordPress.

Enigma 1271: Roman ring

From New Scientist #2429, 10th January 2004

George recalled the junior school word game of turning DOG into CAT and back to DOG, changing just one letter at a time forming a valid English word at each step, without using the same word twice.

He now proposed a similar puzzle using Roman numerals – for example one eight step loop might be:

Enigma 1271

George’s rules are that each “word” must be a valid Roman numeral of six different letters and beginning with “M”. Just one letter is changed at each step.

By analogy with DOG and CAT, George proposes to change the smallest possible Roman numeral within his rules (MCXLIV) to the largest (MDCLXV) and back to MCXLIV in the smallest possible number of steps with no repetition of any numeral.

What is the “Arabic” value of the numeral which comes exactly half way round the cycle from MCXLIV back to MCXLIV?

This completes the archive of puzzles for 2004, which means there is now a full archive of the most recent 10 years of Enigma puzzles from the start of 2004 to the final Enigma at the end of 2013 (510 puzzles).

There are also 244 puzzles from the start of Enigma in February 1979 up to December 1983 (there next puzzle published will complete 1983), bringing the grand total number of puzzles on the site to 755, which is around 42% of all Enigma puzzles.

[enigma1271]

Enigma 242: Sounds Greek

From New Scientist #1388, 15th December 1983 [link]

The three brothers Alpha, Beta and Gamma (who have different ages) get their sums consistently wrong. They all know their facts and do their calculations correctly, but just before they have to state any numerical answer they change it. One of the three brothers halves the number, one squares it, and the other reverses the number (so that 17 becomes 71, and 90 or 9 becomes 9).

I recently asked them their ages.

The eldest of the three whispered his age to the thinnest, who whispered it to Gamma, who whispered it to the youngest, who told me the answer was 27.

The next youngest of the three whispered his age to the tallest, who whispered the answer to Beta, who whispered it to the shortest, who told me the answer was 23.

Finally, the youngest whispered his age to the shortest, who whispered the answer to the thinnest, who whispered it to Alpha, who told me the answer was 16.

Describe the shortest brother (that is, name, age, and what he does to numbers).

It’s three years since I started the site and there are now 750 Enigma puzzles in the archive, all of them solved and almost all of them solved programatically. This puzzle means we have the first 242 puzzles from Enigma’s inception in February 1979 to December 1983 (there are 3 Christmas puzzles to add to complete 1983), and there’s very nearly a full 10 year archive of the most recent 507 puzzles from January 2004 to the end of Enigma in December 2013 (there are also 3 more puzzles from the start of 2004 required to complete this).

This leaves me with just over 1000 puzzles to source, publish and solve, so there are a good few years of Enigma puzzling left.

[enigma242]

Enigma 217: Auntie Greta’s age

From New Scientist #1363, 23rd June 1983 [link]

“You want to know how old I am?” said Auntie Greta to her two nieces. “Well, as you know, your ages (in years) have no common factor higher than 1. My age (in years) is not an exact multiple of the age of either of you, but the square of my age is exactly the average of the cubes of your ages. So I am …”

How many years old?

This puzzle brings the total number of Enigmas on the site to 700. There’s a continuous archive of puzzles from Enigma 1299 on 24th July 2004 until the final puzzle, Enigma 1780 at the end of 2013 (482 puzzles). There is also a continuous archive from the start of Enigma in February 1979, up to Enigma 217 on 23rd June 1983 (217 puzzles), along with a lone puzzle from 2000 this brings us to 700 Enigmas in total, and leaves around 1085 puzzles to source and upload.

In total just over 39% of all Enigma puzzles are now available on the site. I will continue to expand the archive as time and internet connection allow.

Note: I am waiting for a phone line to be connected at my new house, so I only have sporadic access to the internet at the moment.

[enigma217]

Enigma 213: Enigma’s square

From New Scientist #1359, 26th May 1983 [link]

SLA × SLA = ENIGMA
YSSE × YSSE = ENIGMAS

Usual letters-for-digits rules. The same letter is the same digit, different letters are different digits, throughout.

What (in letters) is the result of multiplying YE by EIYIELIGMI?

Note: I am in the process of moving house, so my time and internet connectivity will be constrained over the next couple of weeks. I’ll keep posting puzzles when I can. Normal service will be resumed when the internet comes to Wales.

[enigma213]