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

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.