Dudeney, Amusements in Mathematics Problem 22 A man recently went into a dairyman's shop to buy eggs. He wanted them of various qualities. The salesman had new-laid eggs at the high price of fivepence each, fresh eggs at one penny each, eggs at a halfpenny each, and eggs for electioneering purposes at a greatly reduced figure, but as there was no election on at the time the buyer had no use for the last. However, he bought some of each of the three other kinds and obtained exactly one hundred eggs for eight and fourpence. Now, as he brought away exactly the same number of eggs of two of the three qualities, it is an interesting puzzle to determine just how many he bought at each price.
Suppose he bought N newly-laid at 5d, F fresh at 1d, and E ordinary at Â½d. Then 5N + F + Â½E = 100 and N + F + E = 100. Subtracting gives 8N = E. So N and E cannot be the same. If E and F are the same, then we have N + 8N + 8N = 100, which gives fractional numbers of eggs, so is not possible. If N and F are the same, then N + N + 8N = 100, so N = F = 10 and E = 80, which must be the solution. Dudeney 1-25 (C) John Scholes jscholes@kalva.demon.co.uk 25 Oct 2002