Enigmatic Code

Programming Enigma Puzzles

Category Archives: tantalizer

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?


Tantalizer 496: Anky panky

From New Scientist #1047, 14th April 1977 [link]

Having unearthed a thriving protection racket in the nursery class, Miss Marple summoned the mothers of the six boys concerned to a friendly little chat. She settled the embarrassed ladies equidistantly round a circular table, while she herself paced about lecturing them.

The seating is what concerns us. On Pam’s right sat Mrs Fagin, mother of Yvor. Xerxes’ mum had Ulrich’s mum, Rhona, on her right and Sylvia on her left. Vince’s mum was on Pam’s left and opposite Sylvia. Willy’s mum was opposite Queenie, who sat on Mrs Armstrong’s right. Zacharia’s mother was opposite Mrs Capone. Tess sat opposite Mrs Ellis. Olive was on Mrs Diamond’s left.

Only Mrs Borgia had the guts to blame the whole thing on the school. Can you discover her first name?


Tantalizer 497: My pretty maid

From New Scientist #1048, 21st April 1977 [link]

“How are you travelling, my pretty maid?”
“Not to the South, good sir”, she said.

“Tell you the truth, pray, my pretty maid?”
“Thrice by the end of our song”, she said.

“Then how are you travelling, my pretty maid?”
“East, Sir, or West, kind Sir”, she said.

“But tell you the truth, pray, my pretty maid?”
“Once by the end of our song”, she said.

“And how are you travelling, my pretty maid?”
“West, Sir, or South, dear Sir”, she said.

“And tell you the truth, pray, my pretty maid?”
“Four times by the end of our song”, she said.

“So how are you travelling, my pretty maid?”
“Not North nor South, poor Sir”, she said.

He stood and pondered what she meant.
Can you deduce which way she went?


Tantalizer 498: Check list

From New Scientist #1049, 28th April 1977 [link]

Keen to do their bit for the nation, Aspex Ltd., the aspirin company, have decided to sponsor a chess tournament. There will be four prizes and 13 players will compete on the usual all-against-all basis, with 1 point for each win and ½ for each draw. The prizes will be divisible. Thus if 3 players tie for 1st place they will share the top 3 prizes; if 3 players tie for 3rd place, they will share the 3rd and 4th prizes; and so on.

As you see, there is no telling in advance how many players will end up with a share in the prizes. But my friend George is determined to be among them. Not for him a cliff-hanging struggle for top place, which might leave him prizeless, if boldness does not pay! What he wants to know is exactly how few points he needs to collect from his 12 games to be absolutely sure of featuring on the prize list.

Can you help him?


Tantalizer 499: Kid’s stuff

From New Scientist #1050, 5th May 1977 [link]

Professor Plato once introduced two strangers to each other by saying, “Mrs. Um, I’d like you to meet Mrs. Er, seeing that you are both perfect logicians and mothers with 9 or 10 children between you.”

“How many children do you have?” asked Mrs. Um.
“How many do you have?” Mrs. Er countered.
“How many do you have?” Mrs. Um repeated.
“How many do you have?” retorted Mrs. Er.
“How many do you have?” Mrs. Um persisted.
“How many do you have?” Mrs. Er returned.
“How many do you have?” inquired Mrs. Um.
“How many do you have?” reposted Mrs. Er.

The ladies now fell silent, since, as everyone knows, perfect logicians do not ask questions which they can already answer.

If at least one lady had an even number of children, how many did each have?