Problem Of the week: 22nd May 2023

Dylan Guo

                The evening after national lockdown was lifted, a couple decided to celebrate their newfound freedom at a bar down the street. Much to their surprise, they find four other couples there who had the same idea. Eager for social contact, every person in the five couples enthusiastically hugs each person they had not met before. It turns out that many of the people had actually known each other prior, so when the wife asks everyone how many people they hugged, she remarkably gets nine different answers!

What proportion of the total number of hugs were the wife and her husband involved in?

Try to deal with the couples in pairs, i.e. the number of hugs of each partner in a couple are related.

Start with the extremities.

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