The Ultimate Mathematical Challenge: Over 365 puzzles to test your wits and excite your mind. Литагент HarperCollins USD
Aimee goes to work
Every day, Aimee goes up an escalator on her journey to work. If she stands still, it takes her 60 seconds to travel from the bottom to the top. One day the escalator was broken so she had to walk up it. This took her 90 seconds.
How many seconds would it take her to travel up the escalator if she walked up at the same speed as before while it was working?
78. The pages of a book
The pages of a book are numbered 1, 2, 3, and so on. In total, it takes 852 digits to number all the pages of the book. What is the number of the last page?
79. A letter sum
Each letter in the sum shown represents a different digit.
The letter A represents an odd digit.
What are the numbers in this sum?
80. Timi’s ears
Three inhabitants of the planet Zog met in a crater and counted each other’s ears. Imi said, ‘I can see exactly 8 ears’; Dimi said, ‘I can see exactly 7 ears’; Timi said, ‘I can see exactly 5 ears.’ None of them could see their own ears.
How many ears does Timi have?
81. Unusual noughts and crosses
In this unusual game of noughts and crosses, the first player to form a line of three Os or three Xs loses.
It is X’s turn. Where should she place her cross to make sure that she does not lose?
82. An average
The average of 16 different positive integers is 16.
What is the greatest possible value that any of these integers could have?
83. Painting a cube
Each face of a cube is painted with a different colour from a selection of six colours.
How many different-looking cubes can be made in this way?
84. A Suko puzzle
In the puzzle Suko, the numbers from 1 to 9 are to be placed in the spaces (one number in each) so that the number in each circle is equal to the sum of the numbers in the four surrounding spaces.
How many solutions are there to the Suko puzzle shown?
ACROSS
2. The sum of a square and a cube (3)
4. Nine less than half 26 ACROSS (2)
6. 13 DOWN plus 5 DOWN minus 2 ACROSS minus 10 DOWN (3)
7. A prime factor of (6 ACROSS plus 15) (2)
8. The square root of 4 ACROSS cubed (2)
9. One more than a multiple of 8 (3)
12. Fifteen less than a cube (2)
14. A multiple of fourteen (3)
17. A prime greater than 13 and whose digits are different (2)
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)
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?
86. Palindromic years
The number 2002 is a palindrome, since it reads the same forwards and backwards.
For how many other