For fans of the England soccer team, this summer’s European Championship ended in heartbreak and disappointment. But there is always next year’s World Cup to look forward to – assuming England can qualify.

The team made a decent stab at qualifying when they played Hungary in September 2021 and won the match 4–0.

Ahead of that game, bookmakers were taking bets on the three possible outcomes: a win for Hungary, a draw, or a win for England. The odds offered by three different bookies are shown in Table 1.

Table 1: Odds being offered on the Hungary v. England World Cup qualifying match.

	Bookmaker A	Bookmaker B	Bookmaker C
Win for Hungary	13/7	9/5	17/10
Draw	2/1	7/3	9/4
Win for England	15/8	19/10	33/17

If you were to bet on a win for Hungary with bookmaker C, the odds of 17/10 tell you that you would win £17 for every £10 bet you place should the team be successful. So, let’s say you bet £20 on Hungary to win and they do: the bookie would pay you £54 – that’s your £20 bet returned plus £34 profit.

Now, imagine it is August 2021 – a month before the Hungary v. England game, so you have no idea who is going to win. But you do have £99 to bet with. Based on the odds given in the table, what bets should you place to guarantee yourself a profit? Remember, you don’t know the outcome of the game, so this cannot inform your betting strategy.

Explain to us how you came up with the solution, as we may publish a selection of correct entries (if received by 1 November 2021).

-Puzzle set by Michael Fletcher and published in the October 2021 issue of Significance.

-Try your hand at Michael's previous puzzle, "Higher or lower?" - and see here for the solution (magazine subscription required).

Answer rating: 100% (QA)

Answer You should bet the following amounts Book maker A 33 on Hungary 33 on a draw 33 on England Bo... View the full answer