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Maths Puzzles
 Puzzle 1
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 2
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 3
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).

 Puzzle 4
We have been quite lucky with the weather recently, it has got steadily warmer each day, over the last five days. By this, I mean that the temperature rose by the same amount each day. The average temperature was 2 degrees C and I know it froze on two occasions. I also know the product of the temperatures was over 500 degrees but below 2,000 degrees and each temperature was an integer. What were the last 5 temperatures?

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

The temperatures were -6, -2, 2, 6, 10 degrees C. Each day increased by a steady 4 degrees.

 Puzzle 5
Within the BrainBashers school, the science department has three disciplines. In total, 280 students study chemistry, 254 students study physics and 280 students study biology. 97 students study both chemistry and physics, 138 students study both physics and biology, 152 students study both chemistry and biology. 73 students study all three disciplines. Can you determine how many students there are in the science department? The answer is well below 814.

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

500 students. The answer is most easily seen if three intersecting circles are drawn, and the numbers inside each section worked out.



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