Tantalizer 269: The last trumps

From New Scientist #820, 16th November 1972 [link]

Last night’s final hand at bridge was a tricky one. Reckoning 4 for an ace, 3 for a King, 2 for a Queen and 1 for a Jack, everyone had 10 points. No one had more than one Queen or both red Aces. South and West were void in the same two suits. The King and Queen of clubs were in different hands and so were the King and Queen of diamonds. North had no Kings, and South had no Jacks. East did not hold the Jack of hearts.

Spades were trumps. Who held which of the top four?

This puzzle reappeared as Tantalizer 387.

This puzzle was selected for the book Enigmas (1982), by Robert Eastaway.

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Tantalizer 275: Premonitions

From New Scientist #826, 28th December 1972 [link]

“Methinks I am a prophet new inspir’d”, says John of Gaunt in Act II of Shakespeare’s King Richard II. In the margin against this line in the first folio edition now reposing in the University of Wessex library someone has scribbled in cheap Biro, “So am I. I prophesy that my age on my death will be one twenty-ninth of the year of my birth.”

On the evidence of the handwriting the prophecy is the work of Sir Ambrose Arcane, the noted astrologer. If so, it is yet one more indication of his uncanny powers, since he did indeed die… well, at what age, and in what year?

A variation on this puzzle was published in the book Enigmas (1982), by Robert Eastaway, as follows:

“Methinks I am a prophet new inspir’d”, says John of Gaunt in Act II of Shakespeare’s King Richard II. In the margin against this line in the first folio edition now reposing in the University of Wessex library someone has scribbled in cheap Biro, “So am I. I prophesy that my age on my death will be one thirtieth of the year of my birth.”

On the evidence of the handwriting the prophecy is the work of Sir Ambrose Arcane, the noted astrologer. If so, it is yet one more indication of his uncanny powers.

In the very year predicted, whilst on a pilgrimage to the tomb of the great Tibetan astrologer, Daija Voo, Sir Ambrose tragically contracted smallpox.

In exactly what year, and at what age, was that?

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Tantalizer 387: Fair deal

From New Scientist #937, 20th February 1975 [link]

Here is a little test of your skill at dealing for Bridge. Counting 4 for an Ace, 3 for a King, 2 for a Queen and 1 for a Jack, you must give each player 10 points. No one is to have both red Aces or more than one Queen. The King and Queen of Diamonds are to be in different hands. North is to have no Kings and South no Jacks. South and West are to be void in the same two suits. The King and Queen of Clubs are not to be in the same hand. East is not to have the Jack of Hearts.

Who will get which of the key 16 cards?

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Puzzle 9: The boss’s birthday

From New Scientist #1060, 14th July 1977 [link]

I could not help overhearing an argument the other day between my seven employees, Alf, Bert, Charlie, Duggie, Ernie, Fred and George about the month in which my birthday is. I must admit that I was rather interested in this, for it seemed to be connected with a suggestion about recognising it in some way.

The conversation between them took place on 1st May and it went as follows:

Alf: I have heard him say how wonderful it was having a birthday in a month that started with one of the two letters in the middle of the alphabet. He seems to me rather to over-estimate the advantages of that. In fact I think he is crazy!

Bert: His birthday is not this month or next, but either the one after that or the one after that.

Charlie: I have often heard him say what a disadvantage it has been having a birthday so close to Christmas. This means, I am sure, that it is within two months either way.

Duggie: He told me some time ago that his birthday is in a month with only 30 days.

Ernie: I asked him only the other day and he said it was in October.

Fred: I know that it is not in the winter — i.e. in the last three months or the first three months of the year.

George: You are too late this year; he has had his birthday already.

In fact only one of those statements was true. Which one? Can you say in which month my birthday is? If so, when?

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Puzzle 61: A division sum

From New Scientist #1112, 20th July 1978 [link]

Find the missing digits.

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Puzzle 81: Uncle Bungle and the vertical tear

From New Scientist #1132, 7th December 1978 [link]

It was, I’m afraid, typical of Uncle Bungle that he should have torn up the sheet of paper which gave particulars of the numbers of matches played, won, lost, drawn and so on of four local football teams who were eventually going to play each other once. Not only had he torn it up, but he had also thrown away more than half of it onto, I suspect, the fire, which seems to burn eternally in Uncle Bungle’s grate. The tear was a vertical one and the only things that were left were the “goals against” and the “points” — or rather most of the points, for those of the fourth team had also been torn off.

What was left was as follows:

(2 points are given for a win and 1 for a draw).

It will not surprise those who know my uncle to hear that one of the figures was wrong, but fortunately it was only one out (i.e. one more or one less than the correct figure).

Each side played at least one game, and not more than seven goals were scored in any match.

Calling the teams A, B, C and D in that order, find the score in each match.

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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?

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Enigma 150: Create a crate

From New Scientist #1295, 4th March 1982 [link]

The five-by-five milk crate had some silver-topped bottles, some gold-topped bottles and some empty spaces. The milkman made a note of the contents of the five rows (from left to right in the left-hand picture) and, as a double check, he also made a note of the contents in the five rows in the other direction (from top to bottom in the same picture). He then wrote down his results (with the rows in no particular order), as shown in the right-hand picture.

As you will notice he has forgotten to write down one of the rows.

What should he have written for the remaining row?

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Enigma 145: Vodka on the rocks

From New Scientist #1290, 28th January 1982 [link]

“Did you know that the rate at which the body absorbs alcohol is greatest when the drink is of a certain strength — called the optimum strength?” inquired Professor Drinkwell. “No,” I replied. “What is this optimum strength?” “Its exact value is still open to argument,” continued the Professor, “but you will be all right in assuming it to be one part, by volume, of alcohol in five parts of the drink. Now, vodka is always at least 30 per cent alcohol and so obviously needs to be diluted. In fact, I once calculated that a measure of the vodka you’re drinking needs, in this bar, precisely seven ice-cubes for optimum dilution.” “Won’t they take a long time to melt?” I ventured. “Ah — that’s why I always drink this vodka, which is half as strong as yours. It’s much more practicable to dilute this to optimum strength.” “Oh, how many ice-cubes does it need?” I asked but it was obvious that the vodka had already taken effect for the Professor was already slumped under the table.

How many ice-cubes does the Professor use — and what is the strength of his vodka?

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Enigma 144: Spoiling triangles and quads

From New Scientist #1289, 21st January 1982 [link] [link]

A is a grid of 63 matchsticks. B shows one way of removing 21 matches so as to “spoil” all the triangles in the grid (there are 78 of various sizes) by removing one or more matches from the boundary of each. And C shows a way (an improvement due to Miss Gregory and Mr Buckle on the previously published solution to Enigma 82) of removing 20 matches so as to spoil all the 492 quadrilaterals. The problem now is: what is the smallest number of matches you must remove so as to spoil all the triangles and all the quadrilaterals in A?

Note that C actually has 21 matches removed, although it is possible to solve Enigma 82 by removing only 20 matches (see the diagram attached to my solution).

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Enigma 135: Funny ending

From New Scientist #1279, 12th November 1981 [link]

My children are rabbits at chess but they never play an illegal move. So I was sure that the position, which I found when they had gone to bed last night, must have been legally reached. It looks funny, I grant, but one of them explained what had happened. He had just completed his move and then the cat knocked the circled king off the board and then he had to go straight to bed.

So that makes it all clear. At least it does, if you can answer two questions. What was his last move? And which square was the circled king on, when the cat got it?

According to my dictionary one of the meanings of rabbit is:

• [informal] a poor performer in a sport or game, in particular (in cricket) a poor batsman.

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Enigma 134: Remember, remember

From New Scientist #1278, 5th November 1981 [link]

The fated three sat in “Ye Ink and Blott”
To settle when to carry out the plot.
Said Fawkes “I have this day my passage set:
Before the month is ended I’ll have fled.
Now tell me John and Thomas, if you please,
How many days you’ve free before I leave.”

So John did now the wanted figure state
(The days he’d counted many times of late!)
Tom said he’d three-quarter many days as John
On which he could be there to set the bomb.
“And Tom, I’ve three-quarter many days as thee —
Therefore a handsome choice of dates there’ll be.”

But Guy was wrong since there was just one day
On which all three could be there for the fray.
(One was the smallest number which there could
Have possibly been with the figures as they stood.)
And hence Guy Fawkes did solemnly decree
“The fifth day of November it shall be.”

Tell me, how many days did there remain
Before the day Guy planned to sail away?

This puzzle is a reference to Guy Fawkes, a conspirator in the Gunpowder Plot, the failure of which is traditionally celebrated in Britain on 5th November.

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Enigma 129: Do you really know your tables?

From New Scientist #1273, 1st October 1981 [link]

Using the conventional notation that each letter stands for a different digit the word TABLES can be “topped” by multiplying by three, i.e.:

and “tailed” by multiplying by five, i.e.:

What is the numerical result of multiplying TABLES by seven?

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Enigma 127: King’s rhapsody

From New Scientist #1271, 17th September 1981 [link]

A draughts king stood on square 7 of the draughts board and sighed like a furnace:

“Let’s kiss and love and kiss and love! Love, let’s love and kiss and kiss and kiss! Let’s! Let’s kiss! Let’s kiss! Let’s love and kiss and kiss! Let’s love and love, love and kiss! Let’s kiss and love and …”

At this point he fell down a pit dug by a jealous rival in a square he had not previously visited (hence the abrupt ending). For, as he uttered each word, he had been moving one square diagonally in the direction indicated by the word. Thus “Let’s”, “Love”, “And”, “Kiss” are a code for the four directions a king can move – north-east, south-east, south-west, north-west, although perhaps not respectively.

What is the number of the square with the hole?

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Enigma 125: A great day for the race

From New Scientist #1269, 3rd September 1981 [link]

Fred Betts noticed that there were nine runners in the big race and asked his bookie what odds he was offering.

“3-1 on Bonnie Lass, 4-1 on Golden Stirrup, 7-1 on Two’s a Crowd, 9-1 on Greek Hero and 39-1 the field,” he replied.

Fred thought for a few moments and then astounded the bookie by placing a bet on each of the nine horses, all to win. No each-way nonsense for fearless Fred. And all on credit, of course.

“You might as well give me my winnings now,” said Fred.

“The race hasn’t been run yet, sir,” smiled the bookie.

“That doesn’t matter,” said Fred. “When it has, you’ll owe me £200.”

And he was right.

How much did he stake on each horse?

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Enigma 123: Gnitsugsid

From New Scientist #1267, 20th August 1981 [link]

No Patagonian feast is complete without Gnitsugsid, an arresting dish prepared by the hands of the host in person. It is basically a goulash, simmered in a stock of raspberries, garlic and chocolate and served on a bed of saffron rice topped with bulls’ eyes. So far so good.

There are five special further ingredients, however, and these must be added one at a time in the right order. There is no doubt what they are but mystery shrouds the order. Surviving travellers have contributed five clues but, be warned, only four of them are right. Here they are:

1. The cuttlefish and truffles are both added before the kelp or the mice.
2. The mice and truffles are not added consecutively (in either order).
3. The middle ingredient of the five is either kelp or truffles.
4. Whatever the order of cuttlefish and mice, exactly one ingredient separates them.
5. The mice are added after the truffles and before the bananas.

Well that should be fingerlickin’ good! What is the right order?

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Enigma 116: Very peculiar pairs

From New Scientist #1260, 2nd July 1981 [link]

A peculiar pair of numbers has the property that either added to the square of the other, is equal to a square. And if the pair is very peculiar, the resultant square is the same in each case. For instance, 393/4480 and 4087/4480 are a very peculiar pair because if either number is added to the square of the other the result is (4297/4480)².

We do not insist that the numbers be integers – in fact they cannot be – but they must be positive fractions (not necessarily in their lowest terms).

Can you replace the letters by figures in the following table, so that in each case A² + B = A + B² = C² (with A < B); u < v < w < x; and y < 100.

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Enigma 115: Golden numbers

From New Scientist #1259, 25th June 1981 [link]

Among the riches of King Darius the Great was an amazing quantity of gold ingots. The King kept them stored at the royal treasury, tied up in leather bags and locked in cedarwood boxes. Each bag contained the same number of ingots. Each box contained the same number of bags. There were exactly as many ingots in a bag as there were bags in a box; and exactly as many bags in box as there were boxes in the treasury.

This is all set down in an old parchment, marking the grand count of the ingots for the King’s jubilee. It notes also that the King gave his chief keeper of the treasury a bag of ingots before the count started, thus lessening the previous total by that amount. But the parchment has crumbled, making the new total uncertain. We may be sure, however, that it is two of the following 3-digit numbers, placed side by side to make a 6-digit number:

102, 136, 185, 223, 268, 283, 327, 399.

The question is, how many ingots did the chief keeper receive?

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Enigma 112: Two-square dissection

From New Scientist #1256, 4th June 1981 [link]

5² + 10² = 11² + 2². Can you demonstrate this by cutting the left-hand figure into pieces – as few as possible – which can be reassembled to form the right-hand figure? Cuts should be along the gridlines. It is more elegant not to turn pieces over.

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Enigma 111: Time trouble

From New Scientist #1225, 28th May 1981 [link]

“What’s the time?” gasped Bulldog Drumstick, too groggy to have a clue.

“Something o’clock,” leered Sing Sing, “and now for a test of British intelligence. There is no guarantee that the clock is the right way up. There is no minute hand. The numbers have all been repainted, some or all of them wrong. If you can tell me the time, you can go free. If not the piranhas are peckish.”

“Be a sport and say how many numbers were repainted the same as before.”

“Never! If you knew that, you could deduce the time.”

Our hero then gave him a British uppercut and made his exit. But you, I am sure, would first announce the right time.

What is it?

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