Литагент HarperCollins - The Ultimate Mathematical Challenge - Over 365 puzzles to test your wits and excite your mind

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]

Week 13

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]

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]

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]

88. Multiple missing digits

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

What are the missing digits?

[SOLUTION]

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]

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]

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]

Week 14

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]

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]

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]

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]

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]

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]

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]

Logic Challenge 2

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.

Alby has red hair.

The middle clown in the line-up facing the class has a yellow nose.

Both Jessie and Kenny are wearing yellow shoes.

The clown with yellow hair is standing in between clowns wearing yellow and red shoes.

A clown with a blue nose is next to a clown wearing a blue hat.

Neither Mitch nor Jessie are wearing anything green.

For each clown except Amy, their hat, hair, nose and shoes are different colours.

Kenny’s hat, Jessie’s hair, Mitch’s shoes and Alby’s nose are all the same colour.

The hats worn by the five clowns are all different colours. The same is also true for their hair and noses.

Alby’s hair is the same colour as Amy’s shoes, and Amy’s hair is the same colour as Alby’s shoes.

Everyone except Amy is wearing something that is orange.

[SOLUTION]

Week 15

99. Folded shapes

A sheet of A4 paper (297 mm × 210 mm) is folded once and then laid flat on the table.

Which of these shapes could not be made?

[SOLUTION]

100. Einstein’s clocks

Albert Einstein is experimenting with two unusual clocks that both have 24-hour displays. One clock goes at twice the normal speed. The other clock goes backwards, but at the normal speed. Both clocks show the correct time at 13:00.

What is the correct time when the displays on the clocks next agree?

[SOLUTION]

101. The total area

The diagram shows three semicircles, each of radius 1.

What is the size of the total shaded area?

[SOLUTION]

102. How many weeks?

How many weeks are there in 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 minutes?

[SOLUTION]

103. A platinum question

Platinum is a very rare metal, even rarer than gold. Its density is 21.45 g/cm 3. Assuming that the world production has been about 110 tonnes for each of the past 50 years, and negligible before that, which of the following has a comparable volume to that of the total amount of platinum ever produced?

(a) a shoe box;

(b) a cupboard;

(c) a house;

(d) Buckingham Palace;

(e) the Grand Canyon

[SOLUTION]

104. Underlining numbers