# Can you solve it? World Cup arithmetic

The puzzle that shoots and scores

Hi guzzlers,

The World Cup is almost upon us, so here’s a puzzle to get you in the mood.

England, Tunisia, Belgium and Panama make up Group G. Imagine that once they have all played each other the table looks like this.

If you know only that England beat Tunisia 3-0, can you deduce the score of every other match in the group?

(Clarifications for non football fans: the F column is “goals for”, meaning how many goals the team scored in total; the A column is “goals against”, meaning how many goals the team conceded in total; the P column is “points”, where 3 points are awarded for a win, 1 for a draw and 0 for a loss.)

Foortball table puzzles are a lovely mixture of logical thinking and arithmetic, and like many puzzle types they originated with Britain’s master inventor, Henry Ernest Dudeney. A version of this puzzle appeared in his column in the Strand Magazine in 1921.

A twist on Dudeney’s idea has the table include blanks, as if your coffee spilt on the sports pages and obscured some of the numbers. Here’s one that GCHQ tweeted during Euro 2016:

Again, here you need to work out every result in the group. But to do that you need also to deduce the blanks in the table. It’s quite tricky. If you want a tip to get you going, I’ve included one in the first comment below the line.

The GCHQ soccer-doku led me to ponder whether or not one can design a football table puzzle in which only a single number is given (in other words all the numbers apart from one of them have been obscured) and from which we can deduce every single result between the teams. (Assume that all matches have been played). Is there?

Still on the subject of football puzzles - why is it that England have the worst record at penalty shoot-outs in major tournaments?

In following video Ben Lyttleton and I explain how to take the perfect penalty. Ben and I write the Football School series of books that uses football to explain maths, science, history, psychology and many other subjects. The clip is aimed at 8 to 12-year-olds, and England internationals.

I’ll be back at 5pm UK time with the answers. Please NO SPOILERS.

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

I’m the author of several books of popular maths, including the puzzle books Can You Solve My Problems? and Puzzle Ninja. I also co-write the children’s book series Football School.

Alex Bellos

The Guardian

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