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Category Archives: tantalizer

Tantalizer 400: Loaves and fishes

From New Scientist #950, 22nd May 1975 [link]

A Trappist fête has its drawbacks and its triumphs too. You will see what I mean from an incident at one I attended last week. There was a sea-food stall, selling small items on sticks, where you could buy (in ascending order of price) a whelk, a mussel, a fishcake, a slice of eel and an oyster. While I watched, a party of five monks approached and gave a sign meaning that each of them wanted a different item. (I hasten to add that this was the only untoward sign they made throughout).

Each then placed the same amount of money of the counter. The stall-holder reflected a moment, and then handed each monk the exact item he had wanted. A total of 50 pence then passed across the counter, followed by the return of a total of 16 pence in change. No “tanners” (2½p pieces) were involved.

Assuming that everyone used his loaf and not any extraneous knowledge, what was the price of a fishcake?


Tantalizer 401: The way of all flesh

From New Scientist #951, 29th May 1975 [link]

Professor Pfiffelsammler has been looking into the motivation of cinemagoers. Recently he accosted a line of middle-aged men waiting patiently in the rain to get into “The Way of All Flesh”. The man at the head of the queue said: “There are 39 men behind me. The man at the rear is only here for the smut”. Each other man said: “I am here for the sake of the film’s aesthetic merits. The man in front of me is only here for the smut”.

One tenth of the queue having been admitted, the new front man declared: “There are 71 men behind me”. One ninth of those still waiting were then let in and the new front man said: “There are 15 men behind me”. One eighth of those still waiting were then admitted and the new front man asserted: “There are 27 men behind me”. There were less than 100 men in the queue at the start of the investigation and no one had joined or left (except those admitted into the cinema). Naturally, all and only those there for the aesthetics had spoken the truth. No one, of course, came both for the aesthetics and the smut.

Exactly how man men were there in the queue originally?


There are now 100 Tantalizer puzzles on the site. This means there is a complete archive of New Scientist puzzles from May 1975 – February 1990 and from December 1997 – December 2013, giving a total of about 1569 puzzles on the site. There are 414 Enigma puzzles remaining to fill in the gap from 1990 – 1997, and there are about 220 remaining Tantalizer puzzles in the Google Books archive.


Tantalizer 402: Pairs of knits

From New Scientist #952, 5th June 1975 [link]

One day Snow White taught the seven dwarves to knit. They set to with great delight and each was soon the owner of a fine two-coloured muffler. As each colour of the rainbow was chosen by two dwarves and no two mufflers had the same two colours, the effect was a shade garish. But no one worried about that.

Happy, Dopey, Sleepy and Sneezy flaunted a whole rainbow between them. Happy, Grumpy and Bashful were only one colour short. Doc and Sneezy both chose green. Happy and Sleepy both picked blue. Neither Doc nor Bashful would be seen dead in red and Bashful cannot abide violet. Dopey objects on principle to wearing indigo. Grumpy’s muffler was half yellow and the other half was one of Sleepy’s colours.

Which two chose orange and combined it with what?


Tantalizer 403: Monsters

From New Scientist #953, 12th June 1975 [link]

I don’t know why they bother to put the cornflakes in the cornflake packets. My small son doesn’t even like them. That doesn’t stop the house overflowing with opened packets, however. It’s the monsters, you see. There’s one in every packet and, if you collect a complete set, you get a genuine vampire kit.

So he and his seven best friends are collecting like mad. Indeed they’ve reached a point where any three of them can make a complete set by pooling stock. But you really can’t expect three children to share a vampire kit without squabbling. Two might manage it, I dare say, but just at present there are no two whose combined offerings would make a complete set.

Ah well, we can always give the cornflakes to Oxfam. By the way, how few monsters can there be in a complete set?


Tantalizer 404: Triumvirate

From New Scientist #954, 19th June 1975 [link]

When Ceasar, Pompey and Crassus fell out, the nine scions of the Numerus clan had to decide where their loyalties lay. After much soul-searching three brothers declared for each triumvir.

Of Primus, Secundus and Tertius, only Primus supported Crassus. Quartus sided with Pompey. Quintus made the same choice as Sextus, Septimus or both. Unlike Sextus, Tertius found himself in the same camp as Octavus, Nonus or both. Septimus went the same way as Quintus, Nonus or both. Neither Quartus nor Septimus nor Octavus picked the triumvir favoured by Secundus.

Can you divide the brothers into their trios?


Tantalizer 405: Lucky dogs

From New Scientist #955, 26th June 1975 [link]

Uncle Wilbur was rich enough in life to command the boundless devotion of his family. He repaid them by leaving his entire wealth to be divided equally among the 581 inmates of a dogs’ home. The sum involved ran to five figures and, when divided, it gave each dog a whole number of £s. So that was all right, Best Beloved, do you see?

How much did each dog get? Well, Wilbur had 100 kinsfolk but not all of them survived him. Of those who did he actively disliked most. The exact number of these happens to be the first two digits of the five figure number. The third digit is the number he did not actively dislike. The last two digits is the the sum of the previous groups or, in other words, the number of surviving kinsfolk.

So how much did each dog get?


Tantalizer 406: Two-way traffic

From New Scientist #956, 3rd July 1975 [link]

The slave trade is not what it was, of course, but a man can still scratch a living. Take Sir Henry Barbarossa, the well known TV moralist. Once a month he slips down to a warehouse in Ongar and invests exactly 592 grains of the rare drug alocacoc in white slaves. The girls — mainly suburban au pairs — cost 5 grains each and the boys, being only provincial students, cost 4.

He then ships them to Luvi Dhovi to await the monthly caravan from the interior. There is no telling in advance whether this will have been sent by Sheil Shalimar, who will take up to 40 boys and up to 80 girls, or by Sheik Abednego, who will take up to 80 boys and up to 50 girls. In either event the selling price is 8 grains for each girl and 5 grains for each boy. (All transport and handling costs are paid by the buyer). As slaves don’t keep in that climate, any left over are knocked down to a local merchant for 2 grains each.

Sir Henry prudently budgets for a constant profit, regardless of whose caravan comes. To make this as large as possible, how many slaves of each sex does he buy in Ongar?


Tantalizer 407: Late knight extra

From New Scientist #957, 10th July 1975 [link]

Of the King’s four champions, Sir Albus was the bravest, Sir Bruce, astride Geronimo, the strongest, Sir Caspar, in his purple helm, the proudest and Sir Daniel, with his lilac banner, the craftiest. All were mounted on fine steeds, the knight with the silver shield on Evangeline, he with the orange plume on Furiosus and he with the silver helm on Hercules.

Resplendent too were the hues of their accoutrements. One wore an orange helm and purple shield. One displayed a silver plume and orange shield. One boasted a lilac shield and silver banner. One rejoiced in a lilac helm and purple banner. Sir Caspar’s brother flaunted a lilac plume and orange banner.

“What noble knight is that”, inquired the Queen, “whose purple plume the fitful breezes toss?”.

Can you oblige Her Majesty?


Tantalizer 408: Test question

From New Scientist #958, 17th July 1975 [link]

As a tailpiece to his psychology test Professor Plato invited each of the five candidates to compare the likely performance of three of the others. He got these five pairs of answers:

1. Bill will do better than Edward. Charles will do better than Bill.
2. Debbie will do better than Charles. Arthur will do better than Debbie.
3. Edward will do better than Arthur. Charles will do better than Edward.
4. Bill will do better than Edward. Debbie will do better than Bill.
5. Charles will do better than Bill. Arthur will do better than Charles.

Pleasingly, the winner was wholly right, the boy who came bottom wholly wrong and the others each made exactly one correct prediction. (There were no ties).

What is the order of merit on the professor’s test?


Tantalizer 409: Fe, Fi, Fo, Fum

From New Scientist #959, 24th July 1975 [link]

On the Mount of Mystery dwell those ostraglobulous giants Og, Gog and Magog. They can smell the blood of any Englishman within 400 leagues. So they spotted John Bull as soon as he came within range. But they let him get as far as the bar at the Pig and Whistle, while they finished their elevenses.

Then away they went. Og strode off in his five league boots, Gog in his six league boots and Magog in his seven league boots. Progress was speedy and John got a shock when he chanced to look though the bottom of his mug ten minutes later. Og was a mere nine leagues away, Gog a mere seven and Magog a mere ten.

Without going into gory details, can you say how far it is from the Mount to the Pig and Whistle?


Tantalizer 410: The Clans together

From New Scientist #960, 31st July 1975 [link]

It was a fearsome Hogmany, attended by 11 McSporrans, 11 McTavishes, 11 Mackinnons and 11 MacHinerys. Mind you, that makes it sound worse than it was. The total number present was in fact, smaller, each person being a member of exactly two of the clans.

Especially numerous were those who belonged jointly to the McSporrans and McTavishes. There was no other group which outnumbered them and they outnumbered the McSporran-Mackinnons by precisely two to one.

How many of the company were simultaneously Mackinnons and MacHinerys?

The original puzzle spells “Mackinnon” differently each time it is used.


Tantalizer 411: Diplomatic niceties

From New Scientist #961, 7th August 1975 [link]

When H.M.G.’s five top ambassadors all fell under the same bus, there was an immense fuss about their replacements. The corridors of power hummed with insinuations, until at last a list of five names and a set of conditional agreements was achieved. The latter read:

1. If Sir Basil Brace does not get Paris, Sir Emlyn Entry shall have Bonn or Rome.
2. If neither Sir Ambrose Amble nor Sir Donald Duck gets Washington, Sir Crispin Carruthers shall have Paris.
3. If Sir Ambrose Amble does not get Bonn, Sir Crispin Carruthers or Sir Emlyn Entry shall have Paris.
4. If Sir Donald Duck does not get Rome, then, if Sir Ambrose Amble does not get Paris, Sir Emlyn Entry shall have Moscow.
5. If Sir Ambrose Amble does not get Washington, then, if Sir Donald Duck does not get Moscow, Sir Crispin Carruthers shall have Bonn.

Having been duly warned that “if x then y” does not mean or imply “if not x then not y”, can you assign the top chaps to the right places?


Tantalizer 412: Consider your verdict

From New Scientist #962, 14th August 1975 [link]

While waiting for the judge to settle his wig, sharpen his quill and pump up his cushion, each member of the jury wondered how the 11 others would vote when it came to the point. Here are their predictions in alphabetical order:

Juror A thought all the others would favour acquittal.

Juror B thought all the others would be for convicting.

Juror C thought exactly one of the others would want to convict.

Juror D thought exactly one of the others would want to acquit.

Juror E thought exactly 10 of the others would want to convict.

Juror F thought exactly 3 of the others would want to acquit.

Juror G thought exactly 8 of the others would want to convict.

Juror H thought exactly 7 of the others would want to acquit.

Juror I thought exactly 4 of the others would want to convict.

Juror J thought exactly 8 of the others would want to convict.

Juror K thought exactly 3 of the others would want to acquit.

Juror L thought exactly 9 of the others would want to convict.

In the event all those whose predictions were incorrect voted for one verdict, whereas those (if any) whose predictions were correct voted for the other.

Which jurors favoured acquittal?

A correction (applied to the text above) was published with Tantalizer 416.


Tantalizer 413: Sports day

From New Scientist #963, 21st August 1975 [link]

There were three events after tea and the headmaster appointed Mr Prendergast as bookmaker. After some thought, Prendy produced quite a pretty plan. For a £1 stake you specified the three winners in the order of events (javelin, long jump, hurdles). If you were wholly right, you collected £10. If you got two events right you collected £4. If you were right about the javelin only, you collected £2. Otherwise you lost.

But Prendy had reckoned without Captain Grimes and Dr Fagan (the headmaster), who nobbled all entrants except Clutterbuck, Oglivie and Tangent. Grimes then staked £6 on bets of: CTT; TCC; OTT; COC; OTO; CCO. He made a profit of £4.

The headmaster also staked £6 and naturally did a little better, with a profit of £6 from his bets of: CCT; TOT; OTC; TOC; CTO; OCO.

Which boy won each of the events?

Corrections (applied to the text above) were published along with Tantalizer 414 and Tantalizer 416.

This issue of New Scientist also contains an article about a computer program for solving Tantalizer puzzles using natural language [link].


Tantalizer 414: Three men in a catastrophe

From New Scientist #964, 28th August 1975 [link]

George, Harris and I once decided to acquire a cat apiece. Dear little furry things they were, little bundles of innocence. Or so we thought before we got them home.

But original sin will out and we soon found that none of them was in the least well behaved. George’s was better behaved than the Siamese. The Persian was better behaved than Bubbles. Harris’s was better behaved than Fluff. The Tabby was not worse behaved than the Persian.

All in all we weren’t sorry when Montmorency, the dog, took a hand [paw?] and sent them caterwauling. He took a particularly satisfying bite out of Pollyanna. Whose cat was she?


Tantalizer 415: Dizzy spell

From New Scientist #965, 4th September 1975 [link]

Here is a simple prescription for vertigo. Draw a 4×4 grid (16 cells in a 4×4 array). Write a V in the bottom left corner, an E in each of the two adjacent cells, and R in each of the three empty cells adjacent to an E, a T in each of the four empty cells adjacent to an R, an I in each of the three empty calls adjacent to a T, a G in each of the two empty cells adjacent to an I and an O in the top right corner.

To induce mild vertigo, work out how many ways there are of spelling VERTIGO, starting the the bottom left corner and ending at the top right, as if you were an ant taking exercise. The answer is 20. Feeling better?

Tougher exercise can induce schizophrenia. So start again with a 7×7 grid and repeat the prescription with SCHIZOPHRENIA.

How many ant-like ways are there of spelling that?


Tantalizer 416: Prior arrangements

From New Scientist #966, 11th September 1975 [link]

“This being Wakes Week”, announced the Prior, “I have devised a bit of fun. I shall now paint a red or a blue blob on the pate of each of you for each of the others to see. There will be more red than blue but there will be at least one blue. Each of you is, of course, a perfect logician, and each of you must try to discover your own colour by logic alone. You follow me?”

Eleven tonsured heads nodded gravely and the Prior continued: “On the first stroke of the Compline bell anyone who has already discovered his colour shall leap loudly into the middle of the cloisters for the others to see”. The brothers dispersed and on the first stroke of the bell no one moved a muscle. But when it sounded 24 hours later, an odd number of monks sprang out and cavorted in the cloisters.

How many pates had the Prior painted blue?


Tantalizer 417: King Kong

From New Scientist #967, 18th September 1975 [link]

This ancient Ethiopian game is a sort of Rugby football played with a melon. There are just two ways of scoring. By tossing the melon over a branch of your opponent’s Haha tree you score a King, worth five points. By passing it through his ring of plaited Oompah grass you score a Kong, worth three points. If the match is drawn, each party collects an ox. Otherwise the winner gets two oxen.

Each of the four regions sends its champion to the annual Tourney of the Winds, where each plays a single against each of the others. This year 44 points were scored in total, of which North gained 10, East 15 and South 11. 13 points were scored against North and 9 against East. South drew at least two matches and no two teams received the same number of oxen.

What Kings and Kongs were scored in the match between North and West?


Tantalizer 418: Life in the old dogs

From New Scientist #968, 25th September 1975 [link]

Once a year one-legged parrot-fanciers gather from all over Britain to take part in the Long John Silver Memorial Chess Tournament. Each entrant plays one game against each other, scoring 2 points for each win, 1 for each draw and 0 for each loss. The victor gets 16 men on a dead man’s chess board (yo ho ho) and a bottle of rum.

This year a record 1081 games were played. Each entrant totalled a different number of points, finishing ahead of everyone younger than himself. No one totalled an odd number of points. No two players were the same age.

George was the youngest player to win a game with the King’s Gambit and Henry the oldest to lose one with the Slav defence. All those who played the Slav defence finished ahead of all who played the King’s Gambit.

What was the result of the game between George and Henry?


Tantalizer 419: Wollycobblestones

From New Scientist #969, 2nd October 1975 [link]

There is a fascinating gallstone museum in the Yorkshire town of Wollycobble and folks come from miles around. But it costs a bit of brass to run and there has long been an admission charge. On the principle that the older you are the more interesting other folk’s insides become, the rate is traditionally 1p per year of age. Thus a 10 year old pays 10p, a chap aged 38 pays 38p and so on.

But prices have just had to go up. Yet tradition is sacred. So, craftily, the rate of 1p per year of age remains but now there are only 5p and 7p tickets. As a result the 10 year old still pays 10p (= 5p + 5p) and a 38 year old 38p (= 7p + 7p + 7p + 7p + 5p + 5p); but a 3 year old now pays 5p and an 18 year old 19p (= 7p + 7p + 5p).

The Bundle family makes an annual pilgrimage and, having this year 50 members of all different ages from 1 to 50, arrived expecting to pay £12.75.

At least how much extra did the wily curators extract from them by insisting on the new ticket system?


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