Brainteasers

Age 7-11

Curtain raiser

A teacher collects pound;56 for theatre tickets.

Tickets cost pound;5 for the stalls and pound;7 for the balcony.

The teachers sold some of each ticket.

How many tickets has the teacher sold?

Age 10-14

Raffle tickets

Twelve raffle tickets numbered from 1 to 12 are folded and put in a box.

They are taken out two at a time and the total for each pair is called out.

The totals are 4, 6, 13, 14, 20 and 21.

What are the numbers of each pair of tickets?

Brainteaser solutions from page 30

Curtain raiser

The teacher has sold 7 tickets at pound;5 and 3 tickets at pound;7, a total of 10 tickets

Raffle tickets

The pairs are 1 and 3; 2 and 4; 6 and 7; 5 and 9; 8 and 12; 10 and 11.4 can only be 1 and 3. 21 can be 12 and 9 or 10 and 11, while 20 can be 12 and 8 or 11 and 9. Since all four tickets for 20 and 21 must be different, the only possibility is that 21 is 10 and 11, and 20 is 12 and 8. 9 must be paired with 5 to make 14, or paired with 4 to be make 13. If 13 is 9 and 4, the remaining numbers are 2, 5, 6 and 7, which cannot be used to make 6 and 14. If 14 is 9 and 5, the remaining numbers are 2, 4, 6 and 7, which, when paired, make 6 and 13.

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