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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.
What are the possible values of p?
[SOLUTION] (#litres_trial_promo)
91. A magic square
A 3 × 3 grid contains nine numbers, not necessarily integers, one in each cell. Each number is doubled to obtain the number on its immediate right and trebled to obtain the number immediately below it.
The sum of the nine numbers is 13. What is the number in the central cell?
[SOLUTION] (#litres_trial_promo)
Week 14 (#ulink_6543a76f-befc-57e5-baee-b333ccfcc3c0)
92. A line of coins
Sixty 20p coins are lined up side by side. Every second 20p coin is then replaced by a 10p coin. Then every third coin is replaced by a 5p coin. Finally, every fourth coin in the row is replaced by a 2p coin.
What is the final value of all the coins in the line?
[SOLUTION] (#litres_trial_promo)
93. What is the area?
The figure shows two shapes that fit together exactly.
Each shape is formed by four semicircles of radius 1. What is the total shaded area?
[SOLUTION] (#litres_trial_promo)
94. My children’s ages
The product of my children’s ages is 1664. The youngest is half as old as the eldest.
How many children do I have?
[SOLUTION] (#litres_trial_promo)
95. Tickets for a school play
Tickets for a school play cost £3 for adults and £1 for children. The total amount collected from ticket sales was £1320. The play was staged in a hall seating 600, but the hall was not completely full.
What was the smallest possible number of adults at the play?
[SOLUTION] (#litres_trial_promo)
96. A mini crossnumber
The solution to each clue of this crossnumber is a two-digit number. None of these numbers begins with zero.
Complete the crossnumber.
Across
1. Multiple of 3
3. Three times a prime
Down
1. Multiple of 25
2. Square
[SOLUTION] (#litres_trial_promo)
97. What is ‘abc’?
The letters a, b and c stand for non-zero digits. The integer ‘abc’ is a multiple of 3; the integer ‘cbabc’ is a multiple of 15; and the integer ‘abcba’ is a multiple of 8.
What is the integer ‘abc’?
[SOLUTION] (#litres_trial_promo)
98. The ninth term
In a sequence of positive integers, each term is larger than the previous term. Also, after the first two terms, each term is the sum of the previous two terms.
The eighth term of the sequence is 390. What is the ninth term?
[SOLUTION] (#litres_trial_promo)
Logic Challenge 2 (#ulink_13836ae1-02b9-5754-be71-4e892b48e0e3)
Five clowns are standing in a line. They are being judged as to who is the most colourful clown.
Read the clues below to work out where each clown is standing in the line, and what colour hat, hair, nose and shoes they are wearing. Here ‘left’ and ‘right’ refer to the position in which the clowns appear to someone who is standing facing them.
The blue hat is worn by Jessie.
The red hat is worn by the clown with the blue nose.
Amy has green hair.
Jessie is on the left, at the end of the row, wearing yellow shoes.
Mitch, with yellow hair, has Jessie and Amy next to him.
Kenny is immediately to the right of the clown with red shoes.
