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Programming Enigma Puzzles

11 October 2017

Posted by on **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

notboth 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.

[tantalizer471]

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27 September 2017

Posted by on **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**.

[tantalizer472]

13 September 2017

Posted by on **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?

[tantalizer473]

30 August 2017

Posted by on **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?

[tantalizer474]

16 August 2017

Posted by on **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?

[tantalizer475]

2 August 2017

Posted by on **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?

[tantalizer476]

5 July 2017

Posted by on **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?

[tantalizer477]

28 June 2017

Posted by on **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

ducats to the winner,xducats to the second knight andyto the third.z,xandyare positive descending whole numbers.zTo 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

,xandywere awarded, the being no ties on any day.zThus 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?

[tantalizer478]

14 June 2017

Posted by on **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?

[tantalizer479]

7 June 2017

Posted by on **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?

[tantalizer480]

24 May 2017

Posted by on **From New Scientist #1032, 23rd December 1976** [link]

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

HAPPY CHRISTMAS TO YOU FROM THE NEW SCIENTIST.

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.

[tantalizer481]

4 May 2017

Posted by on **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?

[tantalizer483]

21 April 2017

Posted by on **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?

[tantalizer484]

12 April 2017

Posted by on **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?

[tantalizer485]

29 March 2017

Posted by on **From New Scientist #1037, 3rd February 1977** [link]

Miss Megawatt is one of those sensible people who go to work on an egg. Since variety is the spice of life, she cooks it differently each day but, seeing virtue in routine too, she repeats the same order each working week. She eats no eggs at weekends.

Here are five statements she made recently to a chap from Consumer Research. To keep him on his toes, she included a false one.

1. “On Wednesdays I have it poached or boiled.”

2. “When yesterday’s was coddled, tomorrow’s will be scrambled or vice versa.”

3. “Poached is neither next before nor next after scrambled.”

4. “I coddle and poach earlier in the week than I boil or scramble.”

5. “I scramble earlier than I fry and later than I poach.”What is her order each working week?

[tantalizer486]

22 March 2017

Posted by on **From New Scientist #1038, 10th February 1977** [link]

If you look up the phone number of Sir William Watergate in the book, you will not find it. He is ex-directory. But you can work it out from the list of ten numbers below. Each of the ten has exactly one of Sir William’s digits correctly placed. Consider the first number, 14073, for instance. It implies that Sir William is not on 14257, which would mean two digits correctly placed, nor on 40731, which would mean none.

14073

29402

35862

42936

50811

63136

79588

84771

98174

07145If I just add that Sir William’s true number has five digits, can you discover it?

[tantalizer487]

8 March 2017

Posted by on **From New Scientist #1039, 17th February 1977** [link]

The Smiths have ten children and a dog called Marmaduke. Every so often they buy a huge tin of toffees and them out after tea, one at a time starting with the oldest child. They never miss a child out but whether Marmaduke gets a toffee at every, some or any turn depends on the whim of the moment. Mr and Mrs Smith never take any toffee for themselves.

Now look at it from Marmaduke’s point of view. He never gets one of the first ten toffees. He may or may not get the 11th. He certainly won’t get the 12th, 13th, 14th etc, but he becomes eligible for one at the end of the round, exactly when depending on whether he was lucky or not on the first round.

Now go back to the start of the process with a fresh tin about to be broached. Which is the highest numbered toffee which Marmaduke will certainly not get?

[tantalizer488]

22 February 2017

Posted by on **From New Scientist #1040, 24th February 1977** [link]

Great is the rejoicing in the firm of Furbelows over the engagement of Bertha Button of the button department to Bertie Bow, beau of the bows. Since Miss button is the fanciest of the three spinsters in buttons, while Mr Bow is quite the most eligible of the eight bachelors in the bows, it may seem none too astonishing that Cupid has singled them out. But, considering the number of bachelors in buttons and of spinsters in bows, it is as well that the merry archer does not loose his shaft at random. For, had he done so, the chances are 29 to 23 in favour of an engagement between two members of the same department.

How many bachelors are there in buttons?

[tantalizer489]

16 February 2017

Posted by on **From New Scientist #1041, 3rd March 1977** [link]

Before assuming office as governor of Coconut Island, Sir Donald Duck briefed himself as best he could. There were, he discovered, four chiefs called Fe, Fi, Fo and Fum. The mark of chiefly rank was a turkey feather, red or green at will. The senior chief wore an old pair of Wellington boots and the others went barefoot. Fe always spoke the truth, Fi never, Fo pleased himself and Fum spoke the truth when and only when wearing a green feather.

Knowing no more than this, Sir Donald landed with pomp and found the four chiefs awaiting him. He shook hands all round and inquired, “What is the name of the senior chief?” One chief replied “Fe”, another “not Fum” and a third “Fo”. Sir Donald did not hear the fourth reply but it did not matter, since, being a Balliol man and so very clever, he worked out the name of the senior chief without it.

What was the name of the senior chief?

[tantalizer490]

8 February 2017

Posted by on **From New Scientist #1042, 10th March 1977** [link]

Six proud but ill-acquainted owners were to be heard exchanging remarks at the village pet show. I noted down some of them and off you a brief selection:

Amble to Bumble: “Dimwit keeps a dog”.

Bumble to Crumble: “Egghead and Fumble have pets of the same sort”.

Crumble to Amble: “Bumble’s pet is not the same sort as yours”.

Dimwit to Egghead: “Bumble has the smelliest dog in the village”.

Egghead to Bumble: “Crumble keeps a dog”.

Fumble to Dimwit: “Crumble’s pet is not the same sort as mine.”

Each man has a cat or a dog (not both) and has spoken the truth if and only if addressing someone with the same sort of pet. “Same sort” means merely cat or dog — finer distinctions, such as that between collie and corgi, do not count.

Who owns what?

[tantalizer491]

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