What is the final value of all the coins in the line?
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?
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?
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?
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
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’?
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?
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.
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?
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?
101. The total area
The
