Tshirt Teaser 

The label is now on the outside of his left sleeve 
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Number anagram 

TWO + ELEVEN = THIRTEEN is Nicola's rearranged sum TWO + ELEVEN = THREE + TEN is Claire's reshuffle 
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Can you do it? 

Fill the can to over half full, and tip it so that the water runs out until it reaches just from the lip of the can to the edge of the base, as in the first figure.
Now the can is one half full. Tilt the can upright and mark it inside to show how far the water comes. Finally, tip out the water a bit at a time, until when tilted, the water goes from the mark you scratched to the edge of the bottom, as in the third figure. 
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Polar bearings 

To your left. East is to the right when you travel North, but if you are travelling south (which you must be doing if you are leaving the North Pole) east is to the left. 
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A Minor case 

Watson realized that only children proceed right, right, left, left, right, right ... and only when they are skipping along, which also explains why the footprints are rather scuffed. So the culprit was a child, no doubt one of the family playing an illegal visit to the pantry. 
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Fun run go slow 

It does not matter how fast she runs  even a world record sprint would not increase her average speed to six miles per hour. This is because the Fun Run is three miles long, so if her overall speed was six miles per hour she would do the whole run in 30 minutes. But she has already taken 30 minutes to run the first two miles at four miles an hour, so she would have to run the final mile in zero minutes! (This is a good illustration of the fact that averages can be quite complicated. You usually can't average an average.) 
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Name prediction 

The friend is a man called Peter. For some reason most people assume that Jane's friend must be a woman, even though there is nothing to indicate this is in the puzzle, and even though it is common for college friends to be of the opposite sex. Interestingly, people have the same difficulty when all the sexes in the puzzle are reversed. 
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Mum's secret 

Mum is 49. Weekends account for two sevenths of her age. 
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Turn Four into five 

FOUR into FIVE: it can be done in seven steps: FOUR POUR POUT PORT PORE FORE FIRE FIVE ONE into TWO: using common words it can be done in ten steps: ONE ODE ODD ADD AID LID LIP TIP TOP TOO TWO SEVEN into EIGHT: it is easier to solve this by working backwards from EIGHT, since this is the trickier end. Although lots of common words like MIGHT and FIGHT could come next, they don't seem to lead anywhere. The word that does is BIGHT. Here is our solution in 13 steps: EIGHT BIGHT BIGOT BEGOT BEGET BESET RESET REVET RIVET RIVER RAVER SAVER SEVER SEVEN 
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Magic Beans  

Uncle Norman knew that whatever number of beans were picked up, the number would always finish up at 13 (eight in the right hand and five in the left). For example, if you pick up 15 to start with:
 
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True or False 

Since all of the statements contradict each other, three of them must be false. Therefore statement number three is true and the others are false. 
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Christmas card mystery 

The most likely explanation is that there was a special deal: buy ten cards and get one (or two) free. This means that nobody would buy ten since they might as well take the extra two for the same price. In fact this is a true story: the deal was 50p per card or 12 for £5. So, while buying 5, 15 or 20 cards was cheaper than buying 6, 16 or 21, buying ten was no cheaper than buying 11. 
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Fair prizes 

She won five prizes There were only four girls, and six differences between them which were given. Therefore every possible difference between the four girls was named and we are looking for four numbers whose six differences are 1, 2, 3, 4, 5 and 6. The differences between numbers don't change if all the numbers are increased or decreased by the same amount, so we can start by assuming that the first number is one, in which case the largest number (to give a maximum difference of six), must be seven. We have to fill in the two middle numbers so that the six differences are the numbers 1 to 6. There are just two ways to do this: 1 2 5 7 or 1 3 6 7 The total number of prizes won in the first case is 1+2+5+7=15, which can be raised to 27 if we add three prizes to each girl's total, making their totals 4, 5, 8 and 10. The total of the second set is, however, 17, which cannot be raised to 27 by increasing each number by the same amount. Therefore the number of prizes won by each girl is 4, 5, 8, 10 and Bernice, who won one more than one of the other girls, won five prizes. 
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Byelection blues 

There were ten candidates in total.
This can be worked out with a diagram showing the candidates who are happily married and those who weren't involved in the council scandal.
There are X candidates who are happily married and were not involved in the scandal. We know that only one of these X people was not a 'lunatic fringer' (Henrietta Prigg), so the five other nonlunatics must be Y+Z. (If Y+Z added up to more than 5, then there would be no need for the sixth to be in X either. So the total number of candidates is 8 + Z (=Y+7) The only numbers that fit are Z=2, Y=3, which means there were ten candidates in total.

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Coloured hats 

He says: "I am wearing a black hat." The fourth student reasons as follows: "Suppose my hat is white. The first three students have already tried to work out the colour of their hats and failed. If number two could see white hats on number three and me, then he could deduce his hat must be black (because if it was white, number one would have known his hat was black). But number two said nothing, so if mine was white number three would know that his hat was black. But since number three also said nothing, the only explanation is that I must be wearing a black hat." 
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