Enigmatic Code

Programming Enigma Puzzles

Tag Archives: by: Martin Hollis

Tantalizer 466: Diplomacy

From New Scientist #1017, 9th September 1976 [link]

In the early years of this century, when the lamps were going out all over Europe, Lord Grey asked his advisers whether Bosnia would ally with Austria. They gave thought to the question but could only answer in hypotheticals.

If, they said, Bosnia allies with Austria, Montenegro will ally with Hungary. If Slovakia allies with Denmark, Finland will ally with Serbia. If Albania allies with Slovakia, Poland will ally with Transylvania. If Montenegro allies with Hungary, Latvia will ally with Poland. If Bosnia allies with Austria, then, unless Slovakia allies with Denmark, Finland will ally with Serbia. If Poland allies with Transylvania, Finland will not ally with Serbia. If Latvia allies with Poland then, if Rumania allies with Austria, Poland will ally with Transylvania. If Montenegro allies with Hungary and Albania does not ally with Slovakia, then Rumania will ally with Austria.

They added, of course, that “if x then y” implies neither “if y then x” nor “if not x then not y”. But they could not answer the original question. Assuming all the hypotheticals to be true, can you?



Tantalizer 467: Nine men went to mow

From New Scientist #1018, 16th September 1976 [link]

Nine men went to mow, went to mow a meadow. So write 9 in one of the meadows. One man then went home and the rest went through a gate into the next meadow. Write 8 in that meadow. Another man went home. Write 7 in the next meadow. Then 6, then 5, then 4, then 3, then 2, then 1. Always use a gate. Do not enter the same meadow twice.

Now try adding the three digit number on the top line to that on the middle line. If you have mown the meadows in the right order, they add to the number on the bottom line. If not, go back to the start of the song and begin again. It can be done!

This puzzle was re-published 9 years later as Enigma 328.


Tantalizer 468: Shell fire

From New Scientist #1019, 23rd September 1976 [link]

M. Champignon and M. Escargot are the chefs at the famous Café d’Amour and then have long worked happily together. But lately, alas, they have both fallen in love with the same waitress. They have decided there is only one way to settle the matter. Next Tuesday morning they will take a carton of six fresh eggs and hard boil two of them. The young lady will then replace these two in the carton and reposition them randomly.

This done, Champignon will pick an egg at random and try to break it on his head. If it proves hard boiled, the lady is his. If not, the turn will then pass to Escargot who will pick from the remaining five and try his luck. If he too is crossed in love, both chefs will join the Foreign Legion.

What are the odds that (a) Champignon, (b) Escargot, (c) neither will win the lady?


Tantalizer 469: Revised version

From New Scientist #1020, 30th September 1976 [link]

Mr Chips was sodden with gloom after marking the R.I. test. Admittedly no one had scored nought, which was unusual. (In fact the scores were all different). But, alas, the other pupils had done better than the only four Christians in the class.

After some soul-searching he realised that it was his duty to adjust the marks. So he began by adding to each pupil’s score the number of marks gained in the test by all the other pupils. That was better but the resulting list left something to be desired. So he then subtracted from each pupil’s new score three times his or her original score. That was much more satisfactory. The scores were all positive and totalled 116 marks in all. The heathen Blenkinsop was rightly bottom and could therefore be made to write out the 119th psalm.

How many did Blenkinsop score before and after Mr Chips did his duty?


Tantalizer 470: Thirsty work

From New Scientist #1021, 7th October 1976 [link]

“My formula for life is Wit multiplied by Will”, Uncle Ernest announced for the umpteenth time. “I daresay you don’t know what that gives you, young Tommy”.

“Oh yes I do, Uncle”, Tommy replied cheekily.

“Success”, snapped Uncle Ernest.

“Thirst”, retorted Tommy.

Tommy, of course, had made a cryptarithmetic problem of it:


Each different letter stands for a different digit.

What is the value of THIRST?


Tantalizer 471: Hop, skip and jump

From New Scientist #1022, 14th October 1976 [link]

Hop, Skip and Jump live in different houses in Tantalus St., which is numbered from 1 to 100. Here is what they have to say about the matter:

Hop: “My number is divisible by 7. Skip is much too fat. Jump’s number is twice mine.”

Skip: “Hop lives at 28. My number is one third of Jump’s. Jump and I are not both even.”

Jump: “Hop lives at 91. Skip lives at 81. My number is divisible by 4.”

One of them has thus made three true statements, another three false and the remaining fellow has alternated, uttering either true, false, true or false, true, false.

Who lives where? And is Skip much too fat?

A correction to this puzzle was published with Tantalizer 473. The problem statement above has been revised accordingly.


Tantalizer 472: Regular soldiers

From New Scientist #1023, 21st October 1976 [link]

The republic of Popularia has the largest police force and the longest pedestrator in the world. The latter is a moving pavement which rolls at uniform speed in both directions between the Palace of Justice and the Ministry of Fun. Rolling along with it are armed guards, standing stiffly at attention and posted at regular intervals.

If you too stood at attention on the pedestrator and timed one minute, starting and ending half way between two guards coming the other way, you would be surprised how many guards rolled past you during the minute. Or perhaps you would not. Anyway the number would be eight times the speed of the pedestrator in miles per hour.

You probably long to know the speed of the device. But that is a state secret. So you will have to be content to discover how far apart the guards are posted.

This issue of New Scientist also contains an article of the computer assisted proof of The Four Colour Theorem.


Tantalizer 473: Pigeon post

From New Scientist #1024, 28th October 1976 [link]

In the name of democracy the officers of our Pigeon Fanciers Club announce that they would not stand for re-election this year. This cheered the rest of us no end, until we found that it applied only individually. Collectively they planned to retain all five offices for the umpteenth year running.

To allay suspicions, the plot was a mite complex. There would be no direct swaps. Bumble would take the post of the man who was to become Organiser. Crumble would take the post of the man who was to become Treasurer. Dimwit would take the post of the man who would take Amble’s post. The current Vice-President would take the post vacated by the new President. Eggfrith would become Secretary, despite his wish to become the Organiser.

It all worked flawlessly, of course.

Who was and is what?


Tantalizer 474: Desert crossing

From New Scientist #1025, 4th November 1976 [link]

Able, Baker and Charley all crossed the Great Lunar desert last week. They did not use the same route but each divided his journey into three stages, doing the first by camel, the second by mule and the third on foot.

Able went from P to Q, then from Q to R, then from R to S. Baker’s route was from T to Q, Q to W, W to Y. Charley chose U to Q, Q to V, V to X. All these nine stages are of different length. One man had the longest camel ride, another the longest mule ride and the third walked furthest. One had the shortest camel ride, another the shortest mule ride and the third walked least. In fact Able had the shortest camel ride or the longest mule ride or both.

It is further from P to W via Q than from U to R via Q but not so far as from T to V via Q.

Who walked furthest?


Tantalizer 475: League table

From New Scientist #1026, 11th November 1976 [link]

Here is what is left of the league table pinned in our local church door at the end of the season. It shows the number of goals scored in each match rather than the mere result. Each side played each [other side] once and there were no ties in the “points” list.

You would think that the Anvils, having scored more than half the goals scored in the entire competition, must have done pretty well. But in fact, as you see, they came bottom. The Bears beat the Eagles and drew with the Furies. At least one team drew more games than the Casuals. The Dynamos — but that’s enough information.

Can you fill in the table?


Tantalizer 476: Take your partners

From New Scientist #1027, 18th November 1976 [link]

Amble, Bumble, Crumble and Dimwit had a jolly night of it at the Old Tyme ball. Each took his wife but did not dance with her. In fact each danced only three dances, changing partner each time, and spent the rest of the night in the bar.

In the Cha-Cha Amble danced with a wife larger than Mrs A and Bumble with a wife larger than Mrs B. Then came the rumba, with Crumble in the arms of a wife larger than Mrs C. Then they did the tango, in which Bumble had a wife smaller than Mrs B and Mrs B was squired by a man fatter than Amble. These were the three dances mentioned and no two men swapped partners [with each other] between the Cha-Cha and the rumba or between the rumba and the tango. No two wives are the same size.

What were the pairings for the rumba?


Tantalizer 477: Precognition

From New Scientist #1028, 25th November 1976 [link]

I overheard Professor Foresight discussing the results of a small precognition test the other day. It emerged that he had tossed a penny five times, inviting the thirteen members of his class to write down what was coming before each throw. Six students had done better than the rest, all scoring the same number, although no two had produced identical lists of guesses. Nor had any two of the remaining students produced identical lists.

It also emerged that the penny had not come up Heads all five times. Nor was the actual series Head, Tail, Tail, Tail, Head. Nor was it Tail, Tail, Head, Tail, Tail. At this point the discussion broke up and I was left wondering just what the actual series was. Given that each of these series just mentioned was the guess of one of the unsuccessful seven, can you oblige?


Tantalizer 478: Surprises

From New Scientist #1029, 2nd December 1976 [link]

King Ethelweed needed a new champion. So he commanded his three doughtiest knights to appear before him on the first Monday of the new year and bade them fight one another. They fought all day long until the eventide, when the king called a respite and awarded x ducats to the winner, y ducats to the second knight and z to the third. xy and z are positive descending whole numbers.

To the valiant knights’ dismay, the same happened on the next and each following day, until King Ethelweed at length declared himself satisfied. One each day the same prizes of xy and z were awarded, the being no ties on any day.

Thus it befell that Sir Kay gained the most ducats and became the king’s champion, even though he fared worse on the second day than on the first. Sir Lionel took home twenty ducats in all and Sir Morgan, despite winning top prize on the third day, amassed a mere nine.

Which was the final day and who won how many ducats on it?


Tantalizer 479: Cat and five tales

From New Scientist #1030, 9th December 1976 [link]

Someone let the cat out. Who was it? That is rather hard to decide. Delia says it was one of the twins, meaning Bert or Claud. Alice says it was Bert; and Bert (shame on him!) says it was Claud. Meanwhile Claud says it was Delia; and Emma says it was not Claud.

So it is all a bit of a puzzle and you will be expecting to be told how many of them are right in what they say. But that would make it all much too easy, as you could then deduce who the culprit was. So you will just have to manage with what information you have.

Who let the cat out?


Tantalizer 480: Pitter patter

From New Scientist #1031, 16th December 1976 [link]

When the Olympic games were last held in Patagonia, the Famous torch entered the country at a point exactly 35.27 km from its pedestal in the Olympic stadium. The honour of transporting it from the frontier fell to two Patagonian athletes, Pita and Pata, who were to carry it in turns for the 35.27 km. By presidential decree each was to carry it at each turn any distance he pleased not less than 1 km and not more than 2 km.

Each secretly resolved that he would be the one to carry it the final awesome metre. Since there was nothing in the decree to forbid a different choice of distance at each turn much calculation went on before Pita and Pata tossed for the privilege of having the first turn. In fact Pita won the toss and chose second turn.

Did he chose right?


Tantalizer 481: Happy Christmas

From New Scientist #1032, 23rd December 1976 [link]


Oops! What the message is meant to say is of course:


Perhaps you would like to put it right by sliding on word at a time along a line into a vacant oval. If you are not too saturated with Christmas pud, you should manage it in 26 moves.


Tantalizer 482: Lapses from grace

From New Scientist #1033, 6th January 1977 [link]

An air of rare humility pervades the Common Room at St. Aletheia’s tonight. The seven inmates overdid the post-prandial gin and rashly confessed their sins to one another. Each owned to a different pair of the deadly ones and each sin turned out to have claimed a different pair of victims.

Constance, Emily and Flavia have no sin in common to any two of them. Beatrice, Deborah, Emily and Gertrude confessed to all seven between them. Alice and Gertrude admitted to sloth; Deborah and Emily to lust. Alice is not given to pride nor Beatrice to avarice nor Flavia to either pride or intemperance. Constance, who owned to anger, has a sin in common with Deborah, who did not.

Which pair has fallen prey to intemperance and which pair to envy?


Tantalizer 483: Thought for food

From New Scientist #1034, 13th January 1977 [link]

The food at Dotheboys Hall was always disgusting but that was no problem until the latest rise in the cost of ingredients. So last week Mr Squeers declared that in future it would have to be a great deal nastier.

He sampled it daily, marking it out of 25 for nutrition and out of 25 for expense. Monday was the first day and he awarded his highest total of points in the whole week. The cook was spoken to severely and, gratifyingly, the total awarded on each subsequent day fell daily.

When the totals are broken down under their two headings, things get less simple. Thus Monday was only 4th on each list, 26 points in total were awarded on Tuesday, Wednesday’s menu scored second highest for nutrition, Thursday’s scored 4 points for expense and Friday’s scored 8 for nutrition. Saturday’s was 5th for nutrition and scored 13 for expense. Sunday’s came 6th in the expense list.

There were no ties under either heading and the number of points given on Wednesday for nutrition also occurred somewhere in the expense column.

On which days were the school best nourished and fed at greatest expense?


Tantalizer 484: Blockwork

From New Scientist #1035, 20th January 1977 [link]

Someone gave my small son a bag of 1in cubes for Christmas and he was soon busy stacking them. First he built a rectangular wall one brick thick. Then he used the rest of the bricks to build another rectangular block, using 140 bricks more than the other. Then he got bored.

But I didn’t, as I spotted an intriguing fact. The sum of the lengths of the twelve edges on each construction was the same. So were the total surface areas of the two constructions (including the faces standing on the carpet). All the six dimensions involved were different.

How many bricks had he been given?


Tantalizer 485: Screen test

From New Scientist #1036, 27th January 1977 [link]

Our local cinema has been split into three and the manager has to pick a balanced programme from a list of options supplied by head office. At present he is busy arranging the two weeks after Easter.

He works in whole weeks and here are his thoughts so far. “Sizzling Sixteen” will be shown for at least one week and the Russian “Hamlet” for exactly one week. If “Hamlet” is on for the second week, it will be teamed with that award-winning Western “Dead Fish Gulch” and if  “Hamlet” is on for the first, it will share the billing with “Sizzling Sixteen”. “Tarzan Meets Winnie the Pooh” is a must for the first week, if “Sizzling Sixteen” is screened for the second, and a must for the second, if “Dead Fish Gulch” is not shown in the first. If “Sizzling Sixteen” is to be in the first week, “Dead Fish Gulch” will be in the second. It would be a disaster to screen both “Dead Fish Gulch” and “Sizzling Sixteen” in the first week or both “Dead Fish Gulch” and “Tarzan Meets Winnie the Pooh” in the second.

If the worst comes to the worst, he can fill in with “The Resurrection” in either week or both.

Which three films should he pick for each week?