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Today Puzzle #752

Puzzle No. 752鈥� Tuesday 2nd June

Nicole and Peter are both working parents, currently working from home. They recently saw a study about an unfair share of household tasks between partners (https://www.ifs.org.uk/publications/14861), and they decided to create a schedule of weekly tasks so that they are both happy and equally exhausted. They found 28 essential tasks during the week, among which there is daily cleaning, cooking and doing dishes, and homeschooling the boys from Monday to Friday. They divided labour so that

Nobody does the same task for two consecutive days.

Nobody does more than two tasks a day.

If Peter was cleaning and doing dishes on Monday, which day will he do the laundry?

Today’s #PuzzleForToday has been set by Dr Nicos Georgiou, a senior mathematics lecturer from the University of Sussex.

Click here for the answer

There are 28 tasks. From the description, 7 are cleaning, 7 are doing dishes, 7 are cooking and 5 are home-schooling. This leaves 2 tasks, and from the final question, one of which must be the laundry. Since each parent does no more than two tasks and there are 28 in total for seven days, it must be that each parent does exactly 2 tasks each day.

On weekdays, there are four essential tasks per day so laundry must happen during the weekend. Now, on Monday, Peter cleaned and did the dishes and therefore Nicole must have taught and cooked. This pattern needs to alternate until Friday, since they can’t do the same task for two consecutive days. That means on Friday he still did the dishes and cleaned. On Saturday he now doesn’t have to home-school, which means he has a free task slot. Since we know he must do the laundry by the way the question is phrased, that must happen on the Saturday.

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