16th September 2005 at 01:00
Invisible ink

Max had these five coins. He spent three of them on some invisible ink. How much was the invisible ink?

There are 10 possible answers. Can you find them all?

What if Max has a 50p coin as well? There are 20 possible answers. Find as many of them as you can.


Two cylindrical water tanks, one with a base twice the diameter of the other, are joined at the bottom by a very thin pipe with a tap. The smaller tank is filled with water to a depth of 1 metre.

What will be the common depth of water when the tap is opened?

SOLUTIONS Invisible ink The cost of the invisible ink could be: 35p, 32p, 31p, 27p, 26p, 23p, 17p, 16p, 13p or 8p. It may be easier to think of ways of choosing two of the coins and subtracting the sum of the two coins from 38p, the total of all five coins. If Max has a 50p coin as well, the cost of the invisible ink could be the 10 amounts above, plus 80p, 75p, 72p, 71p, 65p, 62p, 61p, 57p, 56p, 53p.

Two tanks The ratio of the volumes of water when the tap is opened is 1:4, so the common depth is one fifth of the original height, ie 20cm.

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