Читать книгу The Ultimate Mathematical Challenge: Over 365 puzzles to test your wits and excite your mind - Литагент HarperCollins USD, F. M. L. Thompson - Страница 27

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]