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

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Литагент HarperCollins

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Математика

Год написания книги

2018

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A regular octagon is placed inside a square, as shown.

The shaded square connects the midpoints of four sides of the octagon.

What fraction of the outer square is shaded?

[SOLUTION] (#litres_trial_promo)

137. ODD plus ODD is EVEN

Find all possible solutions to the ‘word sum’ shown.

Each letter stands for one of the digits 0−9 and has the same meaning each time it occurs. Different letters stand for different digits. No number starts with a zero.

[SOLUTION] (#litres_trial_promo)

138. Only odd digits

How many three-digit multiples of 9 consist only of odd digits?

[SOLUTION] (#litres_trial_promo)

139. How many tests?

Before the last of a series of tests, Sam calculated that a mark of 17 would enable her to average 80 over the series, but that a mark of 92 would raise her average mark over the series to 85.

How many tests were in the series?

[SOLUTION] (#litres_trial_promo)

140. Three primes

Find all positive integers p such that p, p + 8 and p + 16 are all prime.

[SOLUTION] (#litres_trial_promo)

Crossnumber 5 (#ulink_6f4f13ad-e843-5f09-a109-9e98fe449e11)

ACROSS

1. The cube of a square (5)

4. Eight less than 5 DOWN (3)

6. One less than a multiple of seven (3)

7. A prime factor of 20 902 (4)

10. A number whose digits successively decrease by one (3)

12. Sixty per cent of 20 DOWN (3)

14. A multiple of seven (3)

15. A multiple of three whose digits have an even sum (3)

16. The square of a square (3)

17. A prime that is one less than a multiple of six (3)

19. Eleven more than a cube (4)

22. A number all of whose digits are the same (3)

24. A number that leaves a remainder of eleven when divided by thirteen (3)

25. The square of a prime; the sum of the digits of this square is ten (5)

DOWN

1. A number with an odd number of factors (3)

2. Four less than a triangular number (3)

3. The square root of 9 DOWN (2)

4. A factor of 12 ACROSS (3)

5. The longest side of a right-angled triangle whose shorter sides are 3 DOWN and 4 ACROSS (3)

8. A Fibonacci number (5)

9. The square of 3 DOWN (4)

11. Three more than an even cube (5)

13. A prime factor of 34567 (4)

17. The mean of 10 ACROSS, 16 ACROSS, 18 DOWN, 20 DOWN and 21 DOWN (3)

18. A power of eighteen (3)

20. Two less than 22 ACROSS (3)

21. A number whose digits are those of 12 ACROSS reversed (3)

23. A multiple of twenty-three (2)

[SOLUTION] (#litres_trial_promo)