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[SOLUTION] (#litres_trial_promo)
24. A tennis club
Three-quarters of the junior members of a tennis club are boys and the rest are girls. What is the ratio of boys to girls among these members?
[SOLUTION] (#litres_trial_promo)
25. Rectangles in a square
Five equal rectangles are placed inside a square with side length 24 cm, as shown in the diagram.
What is the area in cm
of one rectangle?
[SOLUTION] (#litres_trial_promo)
26. The absent present
Four children bought a birthday present for their father. One of the children hid the present. When their mother asked them who had hidden the present, the four children made the following statements:
Alfred: ‘It was not me!’
Benjamin: ‘It was not me!’
Christian: ‘It was Daniel!’
Daniel: ‘It was Benjamin!’
It turned out that exactly one of them did not tell the truth.
Who hid the present?
[SOLUTION] (#litres_trial_promo)
27. Professor Brainstorm’s clock
Professor Brainstorm’s clock gains 16 minutes every day.
After she has set it to the correct time, how many days pass before it next tells the correct time?
[SOLUTION] (#litres_trial_promo)
28. What is n?
You are given that n is a positive integer with the property that when we add n and the sum of its digits, we obtain the number 313.
What are the possible values of n?
[SOLUTION] (#litres_trial_promo)
Crossnumber 1 (#ulink_e70c22be-7532-522f-b98f-ccea74072d81)
A crossnumber works just like a crossword except that, instead of filling each square with one of the letters from A to Z, you have to fill each square with a single digit from 0 to 9.
ACROSS
1. The square of an odd number (2)
3. 18 DOWN divided by six (3)
6. A number divisible by three (3)
7. A factor of 14 ACROSS (3)
9. An odd number that is one more than a cube (2)
10. One more than a number divisible by nine (2)
12. A number divisible by both six and a square greater than one (3)
14. A multiple of 7 ACROSS (3)
16. The sum of twice 1 ACROSS and 14 (2)
18. Seven less than a square (2)
19. One more than three times 6 ACROSS (3)
21. A Fibonacci number divisible by seven (3)
22. A palindrome that is twice a prime (3)
23. (9 ACROSS × 4) − 13 DOWN (2)
DOWN
2. A palindrome (3)
3. (3 × 9 ACROSS) − (1 ACROSS + 23 ACROSS) (3)
4. The product of two primes (2)
5. One less than a perfect number (2)
8. A cube that is also a power of two (3)
9. A factor of 6111 (3)
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)
