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#233 An odd league

Set by Howard Williams

The annual football tournament between the teams in the town of Oddhampton has just reached a thrilling climax.

The five teams played each other once, earning two points for a win and one for a draw, with the mathematically pleasing result that four of the teams finished with a different odd number of points.

The spectators were less pleased, however: the number of goals scored was the minimum necessary to produce this result.

What was the total number of goals scored in the tournament?

Solution next week

#232 Opposite number

Solution

Belle lives at number 49.

The total number of houses on the lane, N, must be an odd number (double the number on each side plus the one house at the end). The opposite pairs of houses are numbered 1 and N then 2 and N – 1 and so on. In other words they always add to N + 1, which is an even number. Stan’s number is 45 per cent more than Leah’s, which means Leah’s has to be a multiple of 20. This makes for several possibilities for the pair’s numbers: 20 and 29, 40 and 58, or 60 and 87. Since the two numbers need to add to an even number, Leah and Stan live at 40 and 58, and the house at the end is number 49.