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#109 Chocs-a-weigh

You have been given the job of quality control manager at a chocolate factory and placed in charge of six machines.

Each machine makes chocolate bars that weigh 200 grams. But your predecessor has left you a note to say that one of the machines is creating bars that are 5 grams too light.

Fortunately you have a digital weighing machine at your disposal, which will take weights of up to 3 kilograms.

How can you work out which of the six machines is at fault with just one single weighing – and without breaking any of the chocolate bars?

#108 Half time

Solution

The numbers on the two pieces of the broken clock add up to 69. The numbers 1 to 12 add up to 78, but Sherlock Holmes had observed that one piece added to an odd number and the other to an even number: odd plus even equals odd, so can’t be 78. The only way to achieve two pieces that add up to an odd number is if one of the two-digit clock numbers breaks, so its two digits are on different pieces. This could be 10 (splitting to make 1+0), 11 (1+1) or 12 (1+2). In each case the total of the numbers has decreased by 9, and 78-9=69.