Enigmatic Code

Programming Enigma Puzzles

Category Archives: tantalizer

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 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?


Tantalizer 486: Go to work on an egg

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?


Tantalizer 487: Number system

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.


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


Tantalizer 488: Dog’s life

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?


Tantalizer 489: Buttons and bows

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?


Tantalizer 490: Diplomatic niceties

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?


Tantalizer 491: Cats and dogs

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?


Tantalizer 492: Bon appetit

From New Scientist #1043, 17th March 1977 [link]

If you ever take a holiday on the little island of Mandible, be sure to sample the local food. The basic element is a squash, called a Tiddly, which sells at KL francs per portion. One of these together with a Widdly and an Om make a satisfying meal for LJ francs. But you do not have to have a Tiddly every time and there is much to be said for having just the Widdly and the Om, in which case the dish will cost JL francs. Yet, the Widdly being a bug-eyed lizard and the Om a fried roll filled with peppered ants, you might do well to order a Pom too, thus raising the cost from JL to KM francs. Finally there is the famous Mandible Monster, which consists quite simply of Tiddly, Widdly, Om and Pom and costs MK francs.

Mandible money is straightforward so I have tried to confuse you by replacing digits with letters. Thus JK means 10×J + K and so on.

My own favourite dish is the Tiddly Om Pom (which I had previously supposed to be the French for a drunken man and an apple). In plain digits, what does it cost, given that a Widdly costs J francs more than an Om?


Tantalizer 493: Prize guys

From New Scientist #1044, 24th March 1977 [link]

I met Tom on his way back from the pet show looking pleased with himself. “Prize for my budgie, prize for my cat, prize for my dog”, he explained, “How did Dick and Harry do?”

“Don’t you know?” I asked.

“Not a thing.”

“They too got a prize each for each of a budgie, cat and dog. So you scooped all those nine prizes between you — no ties, incidentally. Dick’s lowest prize was for his budgie.”

“Oho,” exclaimed Tom after reflection, “so Harry did better with his cat than with his dog.”

He then listed all nine prizes correctly. Can you?


Tantalizer 494: Moaning at the bar

From New Scientist #1045, 31st March 1977 [link]

Burpwater’s Best is not the greatest of beers and is to be had only in the five pubs owned by the brewery. The customers are so rude about it that the landlord keeps putting in for transfers. Until four years ago these requests were always refused but there was then a change of policy, resulting in complete annual reshuffles. Now, after four such upheavals, each landlord has had a disgruntled go at running four of the pubs and it at present ensconced in the fifth.

Patrick’s first move was from the Duck to the Anchor and his next to the Cormorant. This second shuffle took Quentin to the Eagle and Roger to the pub previously run by Tony. At the third move Tony handed the Bull over to Roger, who took over from Simon at the following move.

Where is each gloomy publican to be found now?


Tantalizer 495: Bound variables

From New Scientist #1046, 7th April 1977 [link]

Morning coffee at the Logicians’ Union could be with or without any or all of milk, sugar and biscuits. You ordered as you went in by putting your name on any or all of three lists headed “milk”, “sugar” and “biscuits”.

Well, that was not too hard and, by the time Professor Haarschneider was half way through his seminal paper on Semi-opaque Designators, 21 names appeared under each heading. It fell to Professor Nachtwebel, as president, however, to regroup the names into the appropriate seven subsets. Working on the back of an envelope in Polish notation, he found that no two subsets were the same size, that the smallest had three members and that the largest was of those requiring milk but neither sugar not biscuits.

As it was by now the hour appointed for luncheon, the delegates had to forego coffee. How many of those who would have taken sugar were also hoping for biscuits?