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#243 Emmental arithmetic

Set by Alison Kiddle

Chaos reigned during my last visit to Cheese Louise, the local delicatessen. Two customers both claimed to have picked ticket number 6 from the machine that dispenses these to show who is next to be served. For such machines, the numbers appear like those on a calculator.

“You can’t both be number 6,” said Louise, the owner. “One of you must be number 9. I think the only fair thing to do is serve you both after numbers 7 and 8.”

“This system is terrible,” she told me later. “If there are four customers in the shop, there can be a chance of this sort of confusion! A two-digit machine isn’t much better. For example, 12 looks like 21 (see above) if you turn it upside down, so there could be a problem if we have 10 people in the queue. I’m going to buy a three-digit machine!”

With this new machine, how many people would need to be in the queue for there to be a risk of two of them having indistinguishable numbers?

Solution next week

#242 Filling up in Pumpstown

Solution

Yes, there is a strategy that will give me a 50 per cent chance of getting the cheapest fuel. Since the pricing is random, you can glean no information at all from the fact that the first station’s fuel (North) costs 5.83. However, you can improve your chances to 50 per cent by going to the second station (Mid) and checking if the price there is higher or lower than at North. If the price is lower at Mid, then fill up there, but if it is higher, go on to South and fill up there. The possible price orders, cheapest first, are NMS, NSM, MNS, MSN, SNM and SMN. In three of these (MNS, MSN and SNM) sticking at Mid if the price there is cheaper will get you the best deal, giving you a 50 per cent chance of success.