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| 1 |
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I was asked to change a 50p piece. I had more than 50p in my pocket but less than £1, but I could not make exactly 50p. What is the largest amount I could have had in my pocket?
Enter an integer number of pence (e.g. 66)
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p |
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2 |
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A man has the five pieces of chain illustrated in the Figure below. He wants to join them all into one endless chain. It costs 10p to open any link and 20p to weld a link together again. What is the minimum cost?
Enter an integer number of pence (e.g. "66")
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p |
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3 |
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Archimedes, Euclid, Newton and Pythagoras all took the same test. The average score of all four candidates was 16. Archimedes and Euclid had an average of 16, Archimedes and Pythagoras had an average of 13 whilst Euclid and Pythagoras had an average of 18. What was Newton's score?
Enter a single integer, with no spaces (e.g. 99)
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4 |
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What date will it be 2000 days from today?
Enter a date in the format dd/mm/yyyy (e.g. 04/12/2001)
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5 |
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A typical football is made from 12 pentagonal pieces each surrounded by hexagons. How many hexagons are there?
Enter a single integer, with no spaces (e.g. 99)
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6 |
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How many triangles are there in this Figure?
Enter a single integer, with no spaces (e.g. 99)
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7 |
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I am trying to do a rectangular jigsaw puzzle. It contains 1000 pieces in a rectangular grid. I have separated out all the edge and corner pieces and found there were 126 of them. What is the greater number of pieces on an edge of the jigsaw?
Enter a single integer, with no spaces (e.g. 99)
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8 |
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Two squares each of side 20 cm are placed so that the corner of one is in the centre of the other (see the Figure below). Find the area, in cm2, by which they overlap.
Enter a single integer, with no spaces (e.g. 99)
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cm2 |
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9 |
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Which mathematician from the past should have won the SAGA TROPHY?
Enter a name, (e.g. Einstein)
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10 |
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The price of a second-hand car is displayed (in pounds) on 4 cards on the windscreen. Each card shows one digit. The card with the thousands digit blew off in the wind, so the apparent price of the car dropped to exactly one forty-ninth of the intended value. What was the intended price (in pounds) of the car?
Enter the price as a single integer, (e.g. 2500)
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£ |
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11 |
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A computer game is for sale at £80 in November. It increases in price by 30% in December. It is reduced by 30% in January. What is its price, in £, at the end of January?
Enter a value in pounds and pence, separated by a dot (e.g. 123.45)
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£ |
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12 |
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Four children are arguing over a broken toy. Alex says Beryl broke it. Beryl says Chris broke it. Chris and Davinda say they do not know who broke it. Only the guilty child was lying. Who broke the toy? |
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13 |
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How many times are the hands of a clock at right angles to each other on any day between 12 noon and midnight?
Enter a single integer, with no spaces (e.g. 99)
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14 |
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A wall is covered by 160 tiles which are 15cmx15cm. How many 10cmx10cm tiles are needed to cover the same wall?
Enter a single integer, with no spaces (e.g. 99)
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15 |
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Liz and Andy both breed gerbils. If Liz gives Andy one gerbil, Andy will have 3 times as many as Liz, but if Andy gives Liz two gerbils, he will only have twice as many. How many gerbils has Andy got?
Enter a single integer with no spaces (e.g. 123)
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16 |
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Sam thinks of a number, doubles it and adds on 63. The result is the square of the number he first thought of. What was the number he first thought of?
Enter a single integer with no spaces (e.g. 1234)
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17 |
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What is the simplest fraction which has the decimal expansion 0.259259… recurring?
Enter a fraction, consisting of a ratio of integers (e.g. 2/13)
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18 |
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Michael Schumacher sets off 200 metres behind Mika Hakkinen. Mika accelerates at 2 metres per second² and Michael at 3 metres per second². How many seconds elapse before Michael catches up with Mika?
Enter a single integer with no spaces (e.g. 15)
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secs |
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19 |
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An 18cm square of paper is folded in such a way that the bottom right-hand corner P lies at a point 6cm along the left of the top edge (see the Figure below). What is the distance, in cm, from the top right-hand corner to the fold, marked x in the Figure?
Enter a single integer with no spaces (e.g. 15)
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cm |
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20 |
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A regular hexagon is inscribed in a circle which is inscribed in another hexagon. What is the ratio of the area of the large hexagon to the area of the small hexagon?
Enter a ratio in the form a:b, where a and b are integers (e.g. 1:4)
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