Enigmatic Code

Programming Enigma Puzzles

Category Archives: tantalizer

Tantalizer 439: High life

From New Scientist #990, 4th March 1976 [link]

The Enigma Quartet all live on different floors of a mammoth block of flats. Amble and the drummer are on adjacent floors. The harpist lives four floors above Bumble. Crumble and the flautist are ten floors apart.

None of the four lives on a floor served by a lift. For, although there are three lifts all serving floor 0, one stops only at every third floor, one only at every fourth and one only at every fifth. Apart from floor 0, no floor has three lifts stopping.

Since no musician will ever walk up stairs. Amble has no way of visiting the trombonists flat without walking down at least four sets of stairs. Which instrument does Dimwit play and which floor does he live on?


Tantalizer 440: Grunt

From New Scientist #991, 11th March 1976 [link]

Grunt is an after-shave lotion so maddening to women that the wearer can count on at least a broken leg in the rush. How curious then that some mad males are still using Phew. The makers of Grunt are so puzzled that the recently hired Judy the judo champion to look into it.

Judy soon discovered that she found both products equally repellant. So she decided she had better work scientifically. Boarding a strike-bound London bus, all of whose passengers were male, she set to with a questionnaire. Each passenger in turn informed her, “I am using Grunt myself. The man you have just asked is using Phew”. Each, that is, except the first man, who said only, “I am using Grunt”, but added afterwards, “The last man you asked is using Phew”.

Puzzled herself, Judy then asked a few selected passengers how many men were using Phew. The ugliest man said “19”, and then man she had originally interviewed next but three after him said “24”. The fattest said “13” and one she had originally interviewed next but four after him said “28”. The rudest said “24”, and the one she had originally interviewed next but five after him said “13”.

Given that each man used one of the other and that all and only those using Grunt told the truth, can you say how many were using Phew?


Tantalizer 441: Luck of the draw

From New Scientist #992, 18th March 1976 [link]

Dopey confessed that he had never learnt to play chess and was appointed umpire. The other six dwarves settled down to play a five-round tournament. Grumpy drew with everyone but Sneezy and finished equal bottom with Doc, whom he had played in the first round. Sneezy drew with Doc, Happy and Sleepy. Bashful drew with Sleepy. There were no other draws.

There was at least one draw in each round and each dwarf drew in at least two consecutive rounds. The two equal winners did not play each other in the second round.

What were the pairings in the final round?


Tantalizer 442: What’s the score?

From New Scientist #993, 25th March 1976 [link]

The usual five football teams entered our local cup and played the usual one game against each of the others. Exactly three of the games were won by the home side. No two teams won the same number of games. There were no drawn games. Each team played two games at home.

The Ayfield Aces won two games. The Barnley Bears were at home to the Aces and to the Cornfield Casuals. The Casuals were at home to the Aces. Ditching Dynamos were at home to the Eggplant Eagles.

What was the result in each of the ten games?


Tantalizer 443: Roses, roses all the way

From New Scientist #994, 1st April 1976 [link]

Our local council recently planted some white rose bushes but they all died. So they replaced each bush with as many red rose bushes as they had originally planted white bushes. These all died too. Gritting their teeth, the replaced each red bush with as many yellow rose bushes as they had previously planted red bushes. This time they were luckier. Only as many yellow bushes died as red bushes had died before.

Moved by such dogged devotion to horticulture, twelve leading citizens offered to pay for all the surviving yellow bushes, provided that meant that each could pay for the same number of bushes. The Council have lost their record of the number of survivors and do not have the face to spend ratepayers’ money of getting them counted. Yet they would like to know whether they are in a position to accept the offer.

Can you help?


Tantalizer 444: Mutual admiration

From New Scientist #995, 8th April 1976 [link]

At the AGM of the Mutual Admiration Society the six officers go in for a fair bit of self-congratulation. They also pat each other on the back. This is only prudent, since compliments are on a strictly reciprocal basis.

The President had kept above the recent scandal and was loud in his praise of all the others. The Vice-President too had been scarcely involved and felt free to congratulate all but one of his colleagues. The Treasurer, having pocketed so much else, managed to pocket his pride and speak well of four of the others. But the Secretary, the Press Officer and the Master of Ceremonies each omitted two of his comrades for his public list of adulatory mentions.

The Secretary was positively fulsome about the Press Officer. Whom did the Master of Ceremonies fail to praise?


Tantalizer 445: Key problem

From New Scientist #996, 15th April 1976 [link]

Uncle Tom’s bungalow is well endowed with doors, as you can see. He locks them each night, to keep out things that go bump. He would dearly love to do it by passing through each door just once and locking it behind him, so as to finish safely locked up in his bedroom. Alas, it cannot be done. Ah, but wait a minute. It could be done, if he had one of the doors bricked up. By Jove, that’s it.

Precisely which door would he be better without?


Tantalizer 446: Unready reckoners

From New Scientist #997, 22nd April 1976 [link]

Mrs Green and Mrs Brown were conversing about their young in honeyed tones. The topic was prowess at simple arithmetic. Under a mantle of mutually admiring words, they had soon agreed to a duel. The offspring were summoned from the sand pit and set the task of adding seven, three and two.

Little Willie Green wrote done 7 + 3 + 2 = 12 in barely the time it takes to boil an egg. Tommy Brown was still chewing his pencil. Several minutes elapsed before he arrived at SEVEN + THREE + TWO = TWELVE. But Mrs Green’s consoling noises were short lived. Young Tommy, it emerged, had treated the problem as one in cryptarithmetic, with each different letter standing for a different digit.

What was his (correct) numerical rendering of TWELVE?


Tantalizer 447: Marching order

From New Scientist #998, 29th April 1976 [link]

Brother Ambrose, in cell A, desires to visit the chapel, M, for compline. But he belongs to a stern and silent order, which keeps movement and contact to a minimum. No monk may ever enter an occupied room or halt in a corridor. Only one monk may be in movement at any time. Luckily the order is a bit below strength at present and there are only Ambrose, Bernard, Crispin, Ethelbert, Francis, Hadrian, Imogius, Keith and Leo, each in the cell of their letter.

Call it one move when a monk moves from one room to another (possibly passing through other unoccupied rooms). In how few moves can Ambrose get to the chapel, and each other monk return to his own cell?


Tantalizer 448: Love and hate

From New Scientist #999, 6th May 1976

To play this vaguely suggestive game you will need nine cards printed with the words:


You and your opponent take it in turns to pick a word until one of you has collected three with a letter in common. Whoever does so first is the winner.

You lose the toss and your opponent snaps up LOVE. Assuming him to be a master at the game, what must you take to stop him winning?


Tantalizer 449: Gnomes and gardens

From New Scientist #1000, 13th May 1976 [link]

Loose Chippings horticultural club used to be an all-male preserve. But last year a row about whether there should be a prize competition for garden gnomes at the annual show led mysteriously to ladies being allowed to compete in all events. This lapse turned out disastrously, since the Misses Mulch then carried off all the prizes in all the events.

Each sister in fact won exactly two prizes, being the only person to gain prizes in both her successful events and having just one sister who got prizes in neither. Scoring was the usual 3 for 1st prize, 2 for 2nd and 1 for 3rd. Clara (a prize for veg. and the other for cut flowers) tied with Mildred (a prize for fruit and a better prize for shrubs). There were no other ties or any shared prizes and no sister won two prizes in the same event.

Precisely which prizes did Clara and Mildred win? And was there a prize competition for gnomes?


Tantalizer 450: Marriage problems

From New Scientist #1001, 20th May 1976 [link]

We opened the tennis season with a 7-round mixed doubles tourney. The players were 8 married couples and husbands partnered by their own wives throughout. The first round was a match short, as Tania arrived too late. Arthur and wife played Winnie and husband. Round 2 was complete. In it George and Sonia were on different sides of the same net and Bert broke Edward’s service every time.

Dennis and wife beat Sonia and husband in round 3 and Yvonne and husband in round 4. Arthur and wife beat Vera and husband in round 3 and Edward and wife in round 4. Winnie and Xanthippe were opponents in round 6.

Charlie and wife had to rush off just before round 3 and never came back. They would have played Fred and wife in 3, Ursula and husband in 4, Bert and wife in 5 and Arthur and wife in 7.

I see I have not mentioned Harry or Zona. That done, what were the exact (intended) pairings for round 7?


Tantalizer 451: Death rates

From New Scientist #1002, 27th May 1976 [link]

A minor problem which has long troubled medical historians is why two seemingly identical Edwardian TB sanataria in Mercia should have strikingly different death rates. The answer turns out to be simple enough — St. Bede’s in fact had 3,185 more patients than St. Crispin’s.

How did this come to be overlooked? Well, the probable reason is that both were built on the same formula. Each had as many wings as it had wards in each wing and had as many wards in each wing as it had patients in each ward. This was so plainly the whim of some mad bureaucrat that no historian troubled to check whether the number of patients per ward was the same in each place.

So what is the figure in each case?


Tantalizer 452: Snailspaces

From New Scientist #1003, 3rd June 1976 [link]

Four snails set off down the garden path just as dawn broke. Fe and Fi kept pace with each other, a modest but steady shuffle which had taken them a mere eight yards by the time Fo and Fum had reached the rhododendron. Fo was so puffed that he stopped for an hour’s rest and even Fum, who carried straight on, was reduced to the pace of Fe and Fi.

Fo started again just as Fe and Fi came level with him and surged away at his previous pace. Fe promptly accelerated and kept level with him but Fi continued as before. Fe was this one yard ahead of Fi at the end of the path but half an hour behind Fum.

How long is the path?


Tantalizer 453: The school play

From New Scientist #1004, 10th June 1976 [link]

No child was left out of the school play. Each was an angel, a bunny or a demon.

“Were you a bunny, dear?”, Granny asked Tom.
“No”, said Tom firmly.
“He was!”, said Dick.
“He wasn’t!”, said Harry.
“How many of you were bunnies?”, Granny asked.
“Just one”, said Harry.
“Not none”, said Dick.
“More than one”, said Tom.

Any angel had made two true statements, any bunny one and any demon none.

Who was what?


Tantalizer 454: On the cards

From New Scientist #1005, 17th June 1976 [link]

From a complete pack I take two cards chosen from the kings, queens and jacks. I mark one “A” and the other “B”. Your task is to identify A and B, given that the ranking of suits from the top is Spades, Hearts, Diamonds, Clubs and that “if” does not mean the same as “only if”:

1. If A is black, B is a jack.
2. A is a queen, only if B is a diamond.
3. A is a heart, only if B is black.
4. A is a king, if B is a spade.
5. A is a club, if B is a king.
6. A is a heart, if B is a heart.
7. If the higher is a queen, the lower is a heart.
8. The lower is a jack, only if the higher is a heart.
9. If the lower is red, B is a spade.
10. The higher is red, only if A is not a king.


Tantalizer 455: Ballistico

From New Scientist #1006, 24th June 1976 [link]

Ballistico is a wild Guatemalan game for two, played by tossing a dead hen over a barn. The Projecteador (or thrower) stands on one side, the Manudor (or catcher) on the other. If the hen lands within ten metres of the manudor’s position and he fails to catch it, the projecteador scores a ping. Otherwise the manudor scores a pong. Each ping or pong counts as one point.

The players change role after each throw. In other words the projecteador for one throw is the manudor for the next. In the last game I watched 5 pings were scored and the game was won by 7 points to 6.

Was the original projecteador the winner of the loser?


Tantalizer 456: Square deal

From New Scientist #1007, 1st July 1976 [link]

Feeling mortal, Lord Woburn summoned his daughters, Alice and Beatrice, to hear about his will. “I have decided to leave you my hippos”, he announced. “There are either 9 or 16 of them but you do not know which. Each of you will inherit at least one and I shell tell each of you privately how many the other will be getting”.

He was as good as his word. “How many shall I be getting?” Alice asked Beatrice nervously afterwards. Beatrice refused to say but asked, “How many shall I be getting?”. Alice refused to say and again asked, “How many shall I be getting?”. You should know that each lady is a perfect logician, who never asks a question she knows or can deduce the answer to.

I think this proves that a square deal on the hippopotonews is equal to the sum of the squaws on the other two sides. At any rate how many hippos was each to receive?

The puzzle as presented above is flawed, in that the situation described would not arise. An apology was published with Tantalizer 460.


Tantalizer 457: Bee-lines

From New Scientist #1008, 8th July 1976 [link]

Now that Uncle Arthur can’t get about, he watches the world through a sunny little window in the sitting room. It is a diamond-shaped, mullioned window made up of 49 small diamond-shaped panes, separated by lead bars. Just below the window there is a bee hive and sleepy bees are often to be seen ambling up the glass. Uncle Arthur has noticed that they always move in a series of straight lines, passing through the middle of each pane, crossing from pane to pane at the mid point of a bar and moving in an upward direction.

He points out that there are many possible routes a bee can take from bottom to top and would like to know exactly how many.


Tantalizer 458: Knifemen

From New Scientist #1009, 15th July 1976 [link]

If you must have your operation at St. Vitus’ Hospital, choose your surgeon with care. There are four in residence and no two of them are equally safe. Here are six bits of information to cheer you up while you wait:

1. Cutaway is the most lethal.
2. Anyone safer than Borethrough is safer than Axehead.
3. Divot is not the safest.
4. Anyone safer than Divot is no less lethal than Cutaway.
5. Borethrough is not the safest.
6. Anyone safer than Axehead is safer than Divot.

Do I hear you complain that the six statements cannot all be true? Quite right — I put one false one in for diplomatic reasons. And now can you rank the butchers starting with the safest?