Enigmatic Code

Programming Enigma Puzzles

Category Archives: site news

Enigma 648: Piles of fun

From New Scientist #1803, 11th January 1992 [link]

You will need a box of matches. Divide the matches into a number of piles, not necessarily the same number of matches in each pile. For example, you might lay out:

7, 5, 4, 7, 6, 19, 3.

You are allowed to pick any of two piles. If the piles are equal, put them together to make one pile; if the piles are not equal, take from the larger the number of matches that are in the smaller and add them to the smaller.

Using the example above, if you select the 5 and 3, you get:

7, 2, 4, 7, 6, 19, 6.

If you then select the two piles of 6 you get:

7, 2, 4, 7, 12, 19.

If you then select the second 7 and the 19, you get:

7, 2, 4, 14, 12, 12.

You carry on in this way, repeatedly acting on the piles you got from your previous action. Your target is to collect all the matches into one large pile. Sometimes that is possible, sometimes it is not.

For which of the following layouts is it possible to collect all the matches into one pile?

A: 17, 4, 5, 5, 1, 2, 3, 15, 12.
B: 17, 4, 5, 5, 9.
C: 51, 72, 57, 78, 78, 48.
D: 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 23.

News

There are now 1600 Enigma puzzles available on the site. And there are 192 puzzles remaining to post. Which means about 89.3% of all Enigma puzzles are now available.

And between Enigmatic Code and S2T2 there are now 2750 puzzles available.

[enigma648]

Tantalizer 320: Devil’s dice

From New Scientist #871, 8th November 1973 [link]

One perpetual novelty, at least a century old but always good for a fresh marketing under a new name, is the set of four coloured cubes best known as devils dice. If you opened them up and laid them flat, they would look like the diagram, A, B, C and D being the four colours.

According to legend, the devil, always a sportsman, once offered them to a dying sinner as a last chance to save his soul. If the poor lad could stack them in a column each of whose four sides showed four different colours, Old Nick would stay his hand. If, within the obvious time limit, not, then not.

Perhaps you would like to try. Please do not complain at having a diagram instead of the real thing. The diagram makes it easier, at any rate for those wanting to reason it out. It should take about 15 minutes, if you start by asking what each die consists of for purposes of the puzzle.

News

There are now 2700 puzzles available between the Enigmatic Code and S2T2 sites. If you have been playing along and have solved them all, Congratulations!

In total there are 1586 Enigma puzzles available, with 208 puzzles remaining to post. So, about 88.4% of all Enigma puzzles are now available.

[tantalizer320]

2021 in review

[Normally I post the reviews on New Year’s Eve, but this year I am posting it early, in case people have some spare time over Christmas and want to revisit some of the more interesting puzzles of the year that they may have missed. However I will keep the page updated until the end of the year.]

Happy Christmas from Enigmatic Code!

→ [ 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 ]

There are now 1545 Enigma puzzles on the site, along with 177 from the Tantalizer series, all 90 from the Puzzle series, and 141 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 December 1991, and from August 1997 up to the final Enigma puzzle in December 2013, which make up just over 86% of all the Enigma puzzles published. And I have now managed to source all of the remaining 247 puzzles.

In 2021, 102 Enigma puzzles were added to the site (and 48 Tantalizers, 54 Puzzle #s, and 2 others, so 205 puzzles in total).

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

Older Puzzles (from 1991)

::

Newer Puzzles (from 1996)

::

Other Puzzles

::

Sunday Times Teasers

I have also been collecting 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 608 puzzles available on the S2T2 site, 199 were added in 2021.

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

::

Between both sites I have posted 399 puzzles in total this year, bringing the total number of puzzles available to 2557.

Thanks to everyone who has contributed to the sites in 2021, either by adding their own solutions (programmatic or analytical), insights or questions, or by helping me source puzzles from back-issues of New Scientist.

As a bonus New Year puzzle you might like to try inserting mathematical symbols into the following countdown, to make the resulting expression equal to 2022:

10  9  8  7  6  5  4  3  2  1 2022

Here are a couple of solutions:

(10 + 9 + 8) × ((7 + 6 + 5) × 4 + 3) – 21 = 2022
(109) × 8 × (7 + 6) + 5 × (4 + 3 + 2) + 1 = 2022

but there are many others. (I tend to think fewer brackets makes a better solution).

Tantalizer 328: Let us pray

From New Scientist #879, 3rd January 1974 [link]

The six canons at Melchester Abbey take it in turns to preach at Sunday evensong. They preach in alphabetical order — Aumbry, Benedict, Chasuble, Descant, Ember and Fontplug — starting on the first Sunday of the year with Aumbry.

This sounds very handy, as some of them are dreadful bores and it seems that you can plan the Sundays to avoid from the start. But there is a catch. Although the others are as regular as clockwork, old Fontplug is temperamental and there is no predicting at all how many sermons he will in fact give in the year. When he misses out, the turn passes straight from Ember to Aumbry.

In other words, you cannot predict in January who will be preaching the Advent sermon, for instance; but you can name in January at least one man who will certainly not be preaching, say, on the first Sunday in Lent. Somewhere between Lent and Advent, therefore, all predeterminacy is lost. So, looking ahead from the start of January, who is the last man you can be sure will not be preaching on which last Sunday?

This completes the archive of puzzles from 1974. So there is now a complete archive from the start of 1974 up to the end of 1991 (18 years), and also from 1997 to 2013 (17 years). And I’m working on filling in the gaps.

Between Enigmatic Code and S2T2 there are now 2539 puzzles available.

[tantalizer328]

10th Anniversary

Today is the 10th Anniversary of the start of Enigmatic Code.

The first puzzle I posted was Enigma 1674.

There are now 1536 Enigma puzzles posted on the site, and there are (rather neatly) 256 Enigma puzzles remaining to post, as New Scientist wound up Enigma at the end of 2013.

I have recently finished acquiring and transcribing all the missing Enigma puzzles, so I should be able to complete the archive. (Thanks to everyone who has helped in this task).

We also have all 90 puzzles from the Puzzle series (that preceded Enigma) and (currently) 175 of the Tantalizer puzzles (which came before that), and also a few miscellaneous puzzles which have been brought to my attention.

In 2019 I started S2T2, a companion site for Teaser puzzles from The Sunday Times, and there are currently 591 puzzles available there. Which brings the grand total to 2523 puzzles between the sites.

Enjoy!

2500 puzzles!

There are now 2500 puzzles available between the Enigmatic Code and S2T2 sites!

There are 1530 Enigma puzzles available (about 85.6% of all Enigma puzzles published in New Scientist).

And 580 Teaser puzzles (about 18.7% of all Teaser puzzles published in The Sunday Times (so far …)) are available on the S2T2 site.

There is also a complete set of 90 Puzzle puzzles (originally published in New Scientist), and 172 Tantalizer puzzles (of around 500), as well as an up to date set of the new Puzzle # series, currently appearing in New Scientist (132 so far).

All these as well as a few other puzzles that have caught my eye bring the grand total to 2500.

In a couple of weeks we will be celebrating the 10th anniversary of Enigmatic Code, so I’ve averaged just over 250 puzzles a year.

The main thrust of the Enigmatic Code site is to produce an archive of all Enigma puzzles published in New Scientist. I currently have 262 Enigma puzzles remaining to post, originally published 1991 – 1997, and of these I have now transcribed all the remaining puzzles. So it looks like I might eventually reach the goal of having every Enigma puzzle available. Many thanks to the people who have provided me with source material for this task.

Unplanned outage

Apologies for the outage of Enigmatic Code between 08:15 UTC 11th October 2021 and 05:48 UTC on 12th October 2021.

This was due to WordPress.com suspending the site without giving any warning or reason. I immediately contacted them to get the site reinstated.

WordPress.com has now reinstated the site, and apologised for the mistake and any inconvenience caused. Apparently the suspension was due to an automated spam detection system.

It seems an odd way to celebrate the 10th anniversary of the site (coming up in November 2021), but normal service will now resume.

I suppose this is one of the perils of using a free hosting service in order to provide the site for free. But for the most part WordPress.com has performed quite well over the last 10 years, the last couple of days notwithstanding. However I am always interested to hear about other hosting options that may provide a better environment for the site.

Enigma 634: Biscuit routine

From New Scientist #1788, 28th September 1991 [link]

Rosemary was getting tea for 124 visitors. There were 17 biscuits in each packet, and she wanted to buy a number of packets so that each visitor had the same number of biscuits and there was one biscuit left over for her to have after she had washed up.

Rosemary had a routine for finding the answer. First, she calculated that if each visitor had one biscuit, then she would need 7 packets and 5 extra biscuits. She noted the number 5, and looked at the question of 5 visitors and 17 biscuits in each packet. That was easy — she would buy 3 packets, giving 51 biscuits, so that each visitor had 10 biscuits and there was one left over for her. She noted the number 10, and returned to her original question. She gave each of the 124 visitors 10 biscuits, and adding one more for her gave 1241 biscuits, which is exactly 73 packets.

The next day, Rosemary had 53 visitors and 113 biscuits per packet, but the problem was the same, namely, to have one biscuit left over for her.

Because the number of visitors was less than the number of biscuits, she had to include an extra routine. First, she changed to the question of 113 visitors and 53 biscuits per packet. Now she could use her first-day routine, and she found the answer was 32 packets and 15 biscuits per visitor. Next she subtracted the 32 from the 113 to get 81, and the 15 from the 53 to get 38. Then the original question of 53 visitors and 113 biscuits per packet had its answer: 38 packets and 81 biscuits per person.

On the third day, Rosemary had 293 visitors and 119 biscuits per packet. Again, she wanted to buy a number of packets so that each visitor had the same number of biscuits and there was one left over for her. Also, for the visitors’ health, she decided that each one should get less than a packet.

Either by using Rosemary’s routine, or by your own method, calculate the number of packets she should buy on the third day.

News

This brings the total number of Enigma puzzles on the site to 1,500 (with 292 puzzles remaining to post), nearly 84% of all Enigma puzzle published in New Scientist.

For the past year or so I have endeavoured to post 7 puzzles a week between Enigmatic Code and S2T2, so that people who have found themselves with time on their hands because of the pandemic are not at a loose end. However I now find that I need to make time for other things, so I don’t expect to maintain this posting frequency in the future.

However, there are now 2,381 puzzles available between the two sites, so I hope there are enough for people to keep people amused for the time being. (They are weekly puzzles, so that is over 45 years worth).

Happy Puzzling!

[enigma634]

Tantalizer 352: Og, Gog and Magog

From New Scientist #903, 27th June 1974 [link]

Og, Gog and Magog are three fat little professors of Information Science who can often be found hanging about the computer centre at West Wicklewood. Og always tells the truth, Gog never does, and Magog pleases himself.

Knowing only this much, I decided to find out which is which. The obvious point of departure was their visible differences in girth. “What is the name of the fattest of you?” I asked.

“Og”, replied one of them.

“Not Gog”, answered another.

This told me all I needed to know.

Which is really the fattest?

There are now 150 Tantalizer puzzles available on the site. And I have finished transcribing the puzzles currently available in the Google Books archive, which will allow me to continue to post puzzles as far back as 1971.

[tantalizer352]

Enigma 622: Drawaward

From New Scientist #1776, 6th July 1991 [link]

We have just run the tombola stall at our local church fair. We had a certain number of tickets printed, numbered consecutively from 1 upwards. then we folded each one up and put them all in a large bucket. For 20 pence the parishioners could choose a ticket from the bucket. If the number was palindromic (that is, read the same if the digits were written in the reverse order) they won a prize. So, for example, tickets numbered 3 or 77 or 515 won a prize.

I knew that the cautious parishioners would want to know what proportion of tickets were winners, and so I had worked it out in advance. I was able to tell them that at the start an exact whole number percentage of the tickets were winners and that the percentage itself was a palindrome.

This must have made the draw attractive because early on one gentleman asked to buy 1 percent of all the tickets printed, which wasn’t strictly possible. So instead he erred on the generous side and bought £4 worth.

How many tickets were printed?

News

Between Enigmatic Code and S2T2 there are now 2300 puzzles available. Enjoy!

[enigma622]

Tantalizer 366: Ins and outs

From New Scientist #916, 26th September 1974 [link]

The open competition for the Civil Service is a jolly business. Candidates are first asked individually whether they are good at games, prone to incest, able to site an oil field, members of a secret organisation, or related to anyone at the BBC. Then they are herded into groups which have to form a committee to advise the Minister whether to continue to select civil servants by herding candidates into groups which have to form a committee to advise the Minister, etc. …

Well, anyway, as a parting shot, each candidate has to say how many extroverts and introverts there are in his group; not including himself. All and only those candidates whose own character matches that of the chairman of the selectors in this respect, by an astonishing but invariable coincidence, turn out to have got the number exactly right.

In a recent group of seven, Amble thought all the others extroverted. Bumble though all the others introverted. Crumble recorded three extroverts; Dimwit one introvert; Egghead five extroverts; Fumble three introverts; Grumble one extrovert.

Which of these gentlemen has what in common with the chairman?

News

There are now 2200 puzzles available between Enigmatic Code and S2T2. Enjoy!

[tantalizer366]

2020 in review

Happy New Year from Enigmatic Code!

→ [ 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 ]

There are now 1443 Enigma puzzles on the site, along with 129 from the Tantalizer series, all 90 from the Puzzle series, and 87 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 January 1991, and from September 1997 up to the final Enigma puzzle in December 2013, which make up just over 80% of all the Enigma puzzles published. Of the remaining 345 puzzles I have 47 left to source (numbers 901 – 947).

In 2020, 100 Enigma puzzles were added to the site (and 43 Tantalizers, 5 Puzzles (which completes the Puzzle series), 53 Puzzle #s, and 2 others, so 203 puzzles in total).

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

Older Puzzles (from 1989 – 1990)

::

Newer Puzzles (from 1997 – 1998)

::

Other Puzzles

::

Sunday Times Teasers

I have also been collecting 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 409 puzzles available on the S2T2 site, 107 were added in 2020.

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

::

Between both sites I have posted 380 puzzles in total this year, bringing the total number of puzzles available to 2158.

Thanks to everyone who has contributed to the sites in 2020, either by adding their own solutions (programmatic or analytical), insights or questions, or by helping me source puzzles from back-issues of New Scientist.

As a bonus New Year puzzle you might like to try inserting mathematical symbols into the following countdown, to make the resulting expression equal to 2021:

10  9  8  7  6  5  4  3  2  1

Here are a couple of solutions:

(10 + 9) × 8 × (7 + 6) + 5 × (4 × 3 – 2 – 1) = 2021
10
× 9 + 8 × (7 × (6 × 5 + 4) + 3) + 2 + 1 = 2021

but there are many others.

Tantalizer 380: Tribute

From New Scientist #930, 2nd January 1975 [link]

Tantalos of Thrace bowed low before King Xerxes and declared, “I bring your Majesty some goats, more sheep and yet more oxen, may it please your Majesty.”

“How many of each?” inquired the king.

“3150, Sire, …”

“That is satisfactory.”

“… If multiplied together.”

“That is not satisfactory. How many of each dolt?”

“As many in total, when added together, as the number of your Majesty’s wives.”

“I cannot deduce the exact number of each from that, O base Greek. How many of the beast are oxen?”

“Less than half the total, Sire.”

“Now I can deduce the number of each and it is not satisfactory.”

How many of each had Tantalos brought?

News

This completes the archive of Tantalizer puzzles from 1975. So we have a complete archive of puzzles from 1975 – 1989 (15 years), and also from 1998 – 2013 (16 years).

Between Enigmatic Code and S2T2 there are now 2078 puzzles available.

[tantalizer380]

Enigma 949: Farm land

From New Scientist #2104, 18th October 1997 [link]

A retired farmer is selling his land to his neighbours, but retaining the farmhouse as his retirement home. The whole property forms a square, including the smaller square plot in the corner which contains the farmhouse and is not for sale. The three fields, labelled A, B and C are rectangular, all the same shape but different sizes. The farmer is asking the same price per acre for each. If he wants £10,000 for field B, how much does he expect for the three together?

News

This puzzle brings the total number of Enigma puzzles on the site to 1400. There are 392 puzzles remaining to post, and then the archive of Enigma puzzles will be complete.

There are also 90 puzzles from the Puzzle series (complete) and currently 109 puzzles from the Tantalizer series, bringing the total number of puzzles on Enigmatic Code to 1599 (there are also 64 puzzles from the new Puzzle # series, and few other miscellaneous puzzles, so the actual total is a bit more).

Together with the 322 Sunday Times Teaser puzzles on the S2T2 site this brings the total number of puzzles available between the two sites to about 1989, so we are close to having 2000 puzzles available!

[enigma949]

Enigma 953: Neighbourhood watch

From New Scientist #2108, 15th November 1997 [link]

The houses in Acacia Avenue are numbered from 1 to 30. The residents of 12 of these have joined the local Neighbourhood Watch scheme, and are meeting in the local pub to discuss tactics. They decide to appoint a Street Committee of three from among themselves.

Someone suggested, for no convincing reason, that the committee should comprise three residents whose house numbers are in arithmetic progression — that is to say, the difference between the first two numbers is the same as the difference between the higher two.

This was agreed — until they discovered that no such group of three exists among the 12 numbers. This information uniquely determines the 12 numbers — what are they?

News

There are now 1392 Enigma puzzles available on the site, which leaves 400 puzzles remaining to post. Which means about 77.7% of all Enigma puzzles are now available.

[enigma953]

Tantalizer 401: The way of all flesh

From New Scientist #951, 29th May 1975 [link]

Professor Pfiffelsammler has been looking into the motivation of cinemagoers. Recently he accosted a line of middle-aged men waiting patiently in the rain to get into “The Way of All Flesh”. The man at the head of the queue said: “There are 39 men behind me. The man at the rear is only here for the smut”. Each other man said: “I am here for the sake of the film’s aesthetic merits. The man in front of me is only here for the smut”.

One tenth of the queue having been admitted, the new front man declared: “There are 71 men behind me”. One ninth of those still waiting were then let in and the new front man said: “There are 15 men behind me”. One eighth of those still waiting were then admitted and the new front man asserted: “There are 27 men behind me”. There were less than 100 men in the queue at the start of the investigation and no one had joined or left (except those admitted into the cinema). Naturally, all and only those there for the aesthetics had spoken the truth. No one, of course, came both for the aesthetics and the smut.

Exactly how man men were there in the queue originally?

News

There are now 100 Tantalizer puzzles on the site. This means there is a complete archive of New Scientist puzzles from May 1975 – February 1990 and from December 1997 – December 2013, giving a total of about 1569 puzzles on the site. There are 414 Enigma puzzles remaining to fill in the gap from 1990 – 1997, and there are about 220 remaining Tantalizer puzzles in the Google Books archive.

[tantalizer401]

Enigma 960: Squares into squares

From New Scientist #2115, 3rd January 1998 [link]

Harry and Tom were trying to find a set of three 3-digit perfect squares which between them used nine different digits.

Harry found such a set and also discovered that if he took his one unused digit and the three digits of one of his squares he could arrange them to form a 4-digit perfect square.

(1) What was this 4-digit perfect square?

The best that Tom could manage was to find a 2-digit perfect square and two 3-digit perfect squares which between them used eight different digits. But he also discovered that if he took either one of his two unused digits and the digits of either of his two 3-digit squares he could arrange them to form a 4-digit perfect square.

(2) List in ascending order the four 4-digit perfect squares that Tom could form.

News

This puzzle completes the archive of Enigma puzzles from 1998. There is now a complete archive of New Scientist puzzles from the start of 1998 to the end of 2013, and also from June 1975 to January 1990, a total of 1565 puzzles available. There are 414 Enigma puzzles remaining to post.

[enigma960]

Enigma 544b: Little puzzlers

From New Scientist #1696, 23rd December 1989 [link]

Amy, Beth, Jo and Meg decided to give each other pots of marmee-lade for Christmas. Each girl made a number of pots and then divided her pots into three piles, which were not necessarily equal; then she wrapped up each pile, labelled each parcel, and put them under the Christmas tree. The total number of pots involved was between 50 and 100.

We will let the letters A, B, C, …, I stand for the digits 1, 2, 3, …, 9 in some order. Amy gave D/F of her pots to Jo, and C/B to Meg. Beth gave H/G of her pots to Amy, H/A to Jo, and D/G to Meg. Jo gave F/G of her pots to Amy. Meg gave A/B of her pots to Beth, and D/H to Jo.

On Christmas day, each girl opened the three parcels she had received. Amy received H/E of her pots from Beth, and F/E from Jo. Jo received D/I of her pots from Amy, D/H from Beth and D/A from Meg.

Note that all the fractions were in reduced form before letters were substituted (1/2 and 2/3 are in reduced form, whereas 4/8 and 6/9 are not).

What was the total number of pots that were given?

News

This puzzle completes the archive of Enigma puzzles from 1989. There is now a complete archive of New Scientist puzzles from July 1975 to December 1989, and from February 1998 to December 2013, a total of 1553 puzzles. There are 423 Enigma puzzles remaining to post.

[enigma544b] [enigma544]

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.

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