The Ultimate Mathematical Challenge: Over 365 puzzles to test your wits and excite your mind

11. The sum of the digits of 8 DOWN and 21 ACROSS (2)

12. A number divisible by four (2)

13. A prime that is also a Fibonacci number (3)

15. Three times a prime and six greater than a square (3)

17. One less than a multiple of nine (3)

18. A number divisible by three (3)

19. (12 DOWN × 2) − 5 (2)

20. The sum of the digits of 14 ACROSS is one more than twice the sum of the digits of this number (2)

[SOLUTION] (#litres_trial_promo)

Week 5 (#ulink_edbcfc05-2c43-55b7-907c-d10e9646dd84)

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] (#litres_trial_promo)

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] (#litres_trial_promo)

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] (#litres_trial_promo)

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] (#litres_trial_promo)

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] (#litres_trial_promo)

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] (#litres_trial_promo)

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] (#litres_trial_promo)

Week 6 (#ulink_91c7769f-8820-5f25-8bf3-54a1120854da)

36. Digit sum 2001

Which is the smallest positive integer whose digits add up to 2001?

[SOLUTION] (#litres_trial_promo)

37. Seven semicircular arcs

The diagram shows a curve made from seven semicircular arcs, the radius of each of which is 1 cm, 2 cm, 4 cm or 8 cm.

What is the length of the curve?

[SOLUTION] (#litres_trial_promo)

38. Sorting dominoes

Dominoes are said to be arranged correctly if, for each pair of adjacent dominoes, the numbers of spots on the adjacent ends are equal. Paul laid six dominoes in a line, as shown in the diagram.

He can make a move either by swapping the position of any two dominoes (without rotating either domino) or by rotating one domino.

What is the smallest number of moves he needs to make to arrange all the dominoes correctly?

[SOLUTION] (#litres_trial_promo)