### Brain Teasers

# Winning Kebabs

Mad Ade and three friends at the back of the classroom were comparing the numbers of Kebabs they had won at the local Kebab gala. "I've got one more than you", said Mad-Ade. "I've got two more than you", said one friend to another. "I've got three more than you" said one to another. "I've got four more than you" , "I've got five more than you", "I've got six more than you", rang their excited voices, but we don't know who was talking to whom.

If they had won a total of 27 kebabs between them, how many did Mad Ade win?

If they had won a total of 27 kebabs between them, how many did Mad Ade win?

### Answer

Mad Ade won five kebabsThere were only four friends, and six differences between them which were given. Therefore every possible difference between the four friends was named and we are looking for four numbers whose six differences are 1, 2, 3, 4, 5 and 6.

The differences between numbers don't change if all the numbers are increased or decreased by the same amount, so we can start by assuming that the first number is one, in which case the largest number (to give a maximum difference of six), must be seven.

We have to fill in the two middle numbers so that the six differences are the numbers 1 to 6. There are just two ways to do this:

1 2 5 7 or 1 3 6 7

The total number of kebabs won in the first case is 1+2+5+7=15, which can be raised to 27 if we add three kebabs to each friends total, making their totals 4, 5, 8 and 10. The total of the second set is, however, 17, which cannot be raised to 27 by increasing each number by the same amount.

Therefore the number of kebabs won by each friend is 4, 5, 8, 10 and Mad Ade, who won one more than one of the other friends, won five kebabs.

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