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

18. The mean of 5 DOWN, 21 DOWN and 28 ACROSS (2)

19. Three more than a square (3)

22. An even number that is less than 24 DOWN (2)

24. The sum of 9 ACROSS and a multiple of five (3)

26. The difference of two two-digit triangular numbers and also one more than an odd square (2)

28. The first two digits of the square of 17 ACROSS (2)

29. The hypotenuse of a triangle whose shorter sides are 21 DOWN and 20 DOWN (3)

30. The lowest common multiple of 10 DOWN and 15 DOWN (2)

31. A factor of 6789 (3)

DOWN

1. The square of (one more than a multiple of 29) (4)

2. A prime factor of 2008 (3)

3. A Fibonacci number that is one more than 2 ACROSS (3)

5. Two less than 11 DOWN minus 4 ACROSS (2)

10. Eight more than half 4 ACROSS (2)

11. The sum of a Fibonacci number and a triangular number in three distinct ways (2)

13. The number whose digits are those of 31 ACROSS reversed (3)

14. 3 DOWN plus 11 DOWN (3)

15. A multiple of 5 that is less than 16 DOWN (2)

16. A power of 2 that is greater than 4 ACROSS and less than 28 ACROSS (2)

20. The exterior angle, in degrees, of a regular polygon (2)

21. 70 per cent of 30 ACROSS (2)

23. A prime whose digits are increasing consecutive numbers (4)

24. A power of 2 multiplied by a power of 3 (3)

25. Three less than a multiple of seven (3)

27. 11 DOWN plus 15 plus a quarter of 4 ACROSS (2)

[SOLUTION] (#litres_trial_promo)

Week 13 (#ulink_e62ac059-2da8-5d33-aff5-2f1c4c98ab87)

85. The Beans’ beans

The Bean family are very particular about beans. At every meal all Beans eat some beans. Pa Bean always eats more beans than Ma Bean but never eats more than half the beans. Ma Bean always eats the same number of beans as both of their children together and the two children always eat the same number of beans as each other. At their last meal they ate 23 beans.

How many beans did Pa Bean eat?

[SOLUTION] (#litres_trial_promo)

86. Palindromic years

The number 2002 is a palindrome, since it reads the same forwards and backwards.

For how many other years this century will the number of the year be a palindrome?

[SOLUTION] (#litres_trial_promo)

87. Swallowing spiders

It was reported recently that, in an average lifetime of 70 years, each human is likely to swallow around 8 spiders while sleeping.

Supposing that the population of the UK is around 60 million, what is the best estimate of the number of unfortunate spiders consumed in this way in the UK each year?

[SOLUTION] (#litres_trial_promo)

88. Multiple missing digits

The two-digit by two-digit multiplication shown has lots of digits missing.

What are the missing digits?

[SOLUTION] (#litres_trial_promo)

89. Pippa’s visit

Pippa is visiting her grandparents. She spends half the time playing, a third sleeping and the remaining 35 minutes eating.

How long is her visit?

[SOLUTION] (#litres_trial_promo)

90. Possible ps

The eight-digit number ‘ppppqqqq’, where p and q are digits, is a multiple of 45.