| 1. I ask 50 pupils whether they study French or History. 30 study French, 24 study History and 7 study neither. How many study both? |  |
Year 7, 8 and 9 Challenges
| 1. I ask 50 pupils whether they study French or History. 30 study French, 24 study History and 7 study neither. How many study both? | |
2 .
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I
have a 10 pint measure and a 7 pint measure, both of which are unmarked
and an unlimited supply of water. Using only the two measures how can
I get exactly 9 pints into the 10 pint pot?
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3.
Along a long straight road there are 4 towns; Algerham, Brackfield,
Circhester and Digbury in that order. Circhester is 6km from Algerham.
Digbury is 4km from Brackfield. Circhester is 1km nearer to Digbury
than it is to Brackfield. How far is it from Algerham to Digbury?
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| 4. Using the six dominoes shown, form a square so that the total number of dots on each side is the same. |
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5. The diagram shows two planets which are orbiting their sun. Both move clockwise. The outer planet takes 45 years to complete an orbit while the inner one takes 20 years. At the moment the planets are in line with each other and their sun. In how many years will they next form a line with each other and their sun assuming their orbits are circular? |
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6. The key to a code is given by three whole numbers. The key is transmitted from headquarters by three agents each of whom is given the product of two of them. For example, if the key to the code were the numbers 2,3 and 4, the agents would be given the numbers, 6, 8 and 12 as these are the products of the pairs of numbers 2 & 3, 2 & 4, and 3 & 4. The numbers transmitted by the agents are 432, 540 and 720. What are the three numbers that make up the key to the code? |
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