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Maths Puzzle
 Puzzle 1
Yesterday my mother asked me to buy some stamps. Stamps, in the land of BrainBashers, are available in 2p, 7p, 10p, 15p and 20p denominations. For three types of stamp I was asked to buy five of each. For the other two types of stamp, I was asked to buy six of each. Unfortunately I forgot which I was supposed to buy five of and which to buy six of. Luckily my mother had given me the exact money required to buy the stamps, £3.00 and the shopkeeper was able to give me the correct stamps. Which stamps did I buy?

[Ref: ZOKI] © Kevin Stone [Protected Puzzle]

Five lots of 2p, 7p and 15p and six lots of 10p and 20p. The shopkeeper rightly figured that I required five lots of each of the stamps, which came to £2.70, he also knew I required two more stamps which added up to the difference. QED.

 Puzzle 2
At midnight on Sunday, December 31st, Professor Stone set two of his analogue clocks to the correct time. One of his clocks gains one minute every hour and the other loses two minutes every hour.
1. When will the clocks next show the same time as each other?
2. When will the clocks both show the correct time?

[Ref: ZDJB] © Kevin Stone [Protected Puzzle]

1. Midnight after 10 days, which is 240 hours later. They both show 4 o'clock, one clock has gained 240 minutes (4 hours) and the other has lost 480 minutes (8 hours).
2. Midnight after 30 days, which is 720 hours later. They both now show 12 o'clock.

 Puzzle 3
My BrainBashers electronic world atlas has developed a fault, I did a listing of miles from England to particular countries and here is the result:
Spain 14,000 miles
Fiji 12,000 miles
Germany 18,000 miles
Brazil 16,000 miles
How far away did it list Iceland as?

[Ref: ZZKL] © Kevin Stone [Protected Puzzle]

20,000: each vowel is worth 4,000 miles and each consonant is worth 2,000.

 Puzzle 4
A long train, half a kilometre long, is about to enter a long tunnel. The tunnel is 10k long. If the speed of the train is 35kph, how long will it take for the entire train to pass through the tunnel - from the front of the train entering to the end of the train leaving the tunnel?

[Ref: ZRWF]

The train takes 18 minutes. The front of the train has to initially travel 10k to leave the tunnel, and then a further 0.5k until the rear of the train has left the tunnel - a total of 10.5k. Which takes 60 * (10.5 / 35) = 18 minutes.

 Puzzle 5
What does this equation simplify to?
(x - a) * (x - b) * (x - c) * ... * (x - z) = ?

[Ref: ZTDR]

0: since one of the terms is (x - x).



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