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

[SOLUTION] (#litres_trial_promo)

76. What is the unshaded area?

Eight congruent semicircles are drawn inside a square of side length 4.

Each semicircle begins at a vertex of the square and ends at a midpoint of an edge of the square.

What is the area of the unshaded part of the square?

[SOLUTION] (#litres_trial_promo)

77. 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?

[SOLUTION] (#litres_trial_promo)

Week 12 (#ulink_bbb3881f-c648-5399-b549-b7bd973ec51b)

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?

[SOLUTION] (#litres_trial_promo)

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?

[SOLUTION] (#litres_trial_promo)

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?

[SOLUTION] (#litres_trial_promo)

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?

[SOLUTION] (#litres_trial_promo)

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?

[SOLUTION] (#litres_trial_promo)

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?

[SOLUTION] (#litres_trial_promo)

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?

[SOLUTION] (#litres_trial_promo)

Crossnumber 3 (#ulink_b4b21f71-ddf6-546e-a5cf-0fa3cff12984)

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)