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Programming Enigma Puzzles
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:
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.
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?
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).
From New Scientist #2104, 18th October 1997
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?
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!
From New Scientist #2108, 15th November 1997
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?
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.
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?
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.
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.
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.
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?
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.
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.
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:
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.
From New Scientist #2133, 9th May 1998 [link]
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?
There are now 450 Enigma puzzles remaining to post, which means that 75% of all Enigma puzzles are now available on the site.
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.
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.
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.
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 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.
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.
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.
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).
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.
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:
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.
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.
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!
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.