## Brain-Teaser 476

**From The Sunday Times, 12th July 1970** [link]

A football pools fan suggests a novel points scoring system which, he says, is a lot of fun and so easy to do.

For Home wins and Draws the goals for teach match are written down (Home teams first, of course), and the figures placed next to each other. This gives the points. For example, a Home team winning by 10 goals to 3 scores 103 points, a 5-5 Draw 55 points, and so on. You have to select a given number of matches, for example, eight, from the list, which the object of making the highest points score.

I need not tell you about points for Away wins, because I did not include any among my selections when I tried out the system the other day. All my forecasts were correct. They comprised 2 Home Wins, and the remainder were all Draws. One of my Home wins was worth 2 more points than the other Home win. No match had a goals aggregate greater than 16, and the points obtained from my 2 Home wins accounted for exactly 60 per cent of the points obtained from all the matches I selected.

How many points did I score?

[teaser476]

## Jim Randell 8:18 am

on27 April 2019 Permalink |This Python 3 program runs in 93ms.

Run:[ @repl.it ]Solution:Your selection scored 440 points.Possible draws are 0-0, 1-1, …, 8-8, scoring 0, 11, …, 88 points respectively. So draws always score some multiple of 11 points.

There are 16 ways to have two wins that have scores differing by 2, but only one of these gives the remaining 40% of points being a multiple of 11.

That is: wins of 13-1 and 13-3, which have scores of 131 points and 133 points respectively.

Together these give 264 points, which is 60% of a total of 440 points, leaving 176 points to be made up from the draws, and 176 = 16 × 11.

There are 63 ways in which we can choose 5 draws to give a total of 176 points. For example: two 8-8 matches, and three 0-0 matches.

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