You return from foreign parts having contracted the dreaded lurgy. Your doctor – an accurate and careful practitioner – gives you four weeks’ supply of Grongebladder tablets and, to combat the terrible side-effects, four weeks’ supply of Gargol tablets. You must (religiously!) take one of each daily.
Now the tablets all look exactly the same, and so when on the 13th day you distractedly take out one tablet of one kind and two of the other, you only realise what you must have done when you see the 3 tablets lying there in the palm of your hand. You must have two of one and one of the other, but can’t tell which is which.
Now it would be fatal to take two Grongebladder tablets, or two Gargol tablets on the same day. It would be fatal to take one of them without the other. You have to take one of each. How do you sort matters out without getting more tablets?
Each issue, we award a prize to three lucky winners – this time we have copies of AC Grayling's secular bible The Good Book. You can send us your answers (complete with your postal address, if you want to win) to editor[at]newhumanist.org.uk. Deadline is 1 June 2011. We will publish the solution alongside next issue's quiz.
Solution to the March/April Quiz, "No eggs/pence spared"
Imagine reversing the procedure of crossing the 7 bridges. Each time d’Artagnan retraces his steps over a bridge he receives half an egg back and then has the number of his eggs doubled. So if he ended up with x (eggs or pence) he must have had (x + 1/2) X 2, which is 2x + 1, just before crossing that bridge. Similarly, before the 6th bridge he must have had 4x + 2 + 1. Before the 5th bridge he must have had 8x + 4 + 2 + 1. The pattern is clear. Before crossing the 7th bridge he must have had 128x + 64 + 32 + 16 + 8 + 4 + 2 + 1, or 128x + 127. As he ended up with 12 eggs he must have bought (128 X 12) + 127 = 1663 eggs for 1663 pence from his brother-in-law. But to arrive at his brother-in-law’s with 1663 pence he must have set off with (128 X 1663) + 127 = 212991 pence. That’s £2,129.91 to us.
