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#236 Picky eaters

Set by Brian Hobbs

My young kids don’t mind helping to carry in the groceries, especially in pursuit of the ultimate prize: getting to be the one who pushes the button that closes the automatic rear door of our minivan. So, as they go back and forth carrying the groceries to the house, I have told them that the one who takes the last item or bag out of the van gets to close the door.

Today, two of my children are with me, and we have just arrived home with a big bag of potatoes, two boxes of fizzy drink and three bags of general groceries. They can carry at most two grocery bags at once (amateurs), two boxes of fizzy drink at once or the heavy bag of potatoes all by itself. Because of how each item is carried, they can only take one type of container at a time, so they won’t be able to carry a case of soda and a grocery bag on one trip.

They will take turns carrying one or two items into the house, and Georgia gets to go first. What should she pick to ensure that she takes the last item and gets to push the magic button?

Solution next week

#235 Sneak a peek

Solution

You need to buy five sneak-peeks if you want to guarantee winning the prize.

There are various ways to do this. For example, look under pots 2, 4, 6 and 8. If one of them (e.g. 4) has a key, spend your last peek on one of its neighbours (e.g. 5). You will then know if the keys are under 4 and 5 or 3 and 4. If none of 2, 4, 6 or 8 has a key, the keys must be under 9 and 10. Another strategy is to choose 2, 5, 6 and 9. If none has a key, spend your last peek on one of the remaining pots (aside from 1 and 10) to decide if the keys are under 3 and 4 or 7 and 8.