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#80 Vive la Diff茅rence

The eccentric manager of Bistro Vive la Diff茅rence has a bizarre method of offering discounts to his customers.

Each seat has a number and each customer gets a discount (in euros) equal to the difference between the numbers of the seats either side of them. For example, a guest seated between seats 6 and 1 would get a discount of 鈧�5 on their meal.

Seven friends have booked a meal, and arrive to find chairs numbered 1 to 7 in order around their table. They figure that with the seats arranged like this, they can get a combined discount of 鈧�20. But they reckon they can do better. They want to maximise their discount, but only have time to swap two chairs before the waiter comes to take their order. Which chairs should they swap?

#79 Marathon relay

Solution

Whoever hands over the torch with 4 miles to go can be certain to have it for the final mile.

To guarantee that they will have the torch at this point, that runner should hand over the torch at 8 miles to go鈥� and before that, at 12, 16, 20 and 24 miles to go.

So Rimsky should take the torch first, run 2.2 miles and hand it over with 24 miles still to go, guaranteeing he will have it for the final mile.