Three friends, eight beers: how to split a bill fairly

Puzzle. Peter, James, and Emma decide to go out for drinks and agree to share the cost equally. At the start of the evening, Peter buys 5 bottles of beer at £3 each. Later on, James buys 3 more bottles at the same price. At the end of the night, Emma hands £7 to Peter and £1 to James, stating that they are now even. Peter gladly agrees, but James feels he's been shortchanged. Who is correct?

Solution. Typically, when friends split expenses on a night out, they assume that reimbursements should be proportional to contributions. However, this overlooks a key point: part of that spending also covers their own share, which changes the calculation entirely. As a result, people often misjudge what a fair split looks like. Fortunately, there’s a simple way to divide costs correctly without awkwardness or disagreement. This is the method Emma used; you can apply it the next time you’re out with your friends.

· Total money spent is £3 x 8 = £24.  

· Each should pay an equal share of £24 ÷ 3 = £8.  

· Peter contributed £3 x 5 = £15, so his refund is £15 - £8 = £7.·  

· James contributed £3 x 3 = £9, so his refund is £9 - £8 = £1.  

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Reimbursing the others left Emma paying a total of £7 + £1 = £8, bringing everyone’s share to an equal amount. This quick and simple calculation ensures a fair split and helps avoid any hard feelings.