Читать книгу The Ultimate Mathematical Challenge: Over 365 puzzles to test your wits and excite your mind - Литагент HarperCollins USD, F. M. L. Thompson - Страница 14

Week 5

29. Turbo the tortoise

Usain runs twice as fast as his mum. His mum runs five times as fast as his pet tortoise, Turbo. They all set off together for a run down the same straight path.

When Usain has run 100 metres, how far apart are his mum and Turbo the tortoise?

[SOLUTION]

30. Rolling a cube

A cube is being rolled on a plane so it turns around its edges. Its bottom face passes through the positions 1, 2, 3, 4, 5, 6 and 7 in that order, as shown.

Which of these two positions were occupied by the same face of the cube?

[SOLUTION]

31. Small change

My bus fare is 44p. If the driver can give me change, what is the smallest number of coins that must change hands when I pay this fare?

[The coins available are 1p, 2p, 5p, 10p, 20p, 50p, £1 and £2.]

[SOLUTION]

32. Eight factors

The number 78 has exactly eight factors, including 1 and 78.

Which is the smallest integer greater than 78 that has eight factors?

[SOLUTION]

33. A small sum

In the addition sum ‘TAP’ + ‘BAT’ + ‘MAN’, each letter must represent a different digit and no first digit is zero.

What is the smallest sum that can be obtained?

[SOLUTION]

34. A circle on a grid

A circle is added to the grid shown.

What is the largest number of dots that the circle can pass through?

[SOLUTION]

35. Numbers around a circle

Five integers are written around a circle in such a way that no two or three consecutive numbers have a sum that is a multiple of 3. Of the five numbers, how many are themselves multiples of 3?

[SOLUTION]