A country woman carrying eggs to a garrison, where she had three guards to pass, sold at the first half the number she had, and half an egg more; at the second, the half of what remained, and half an egg more; and at the third, the half of the remainder and half an egg more; when she arrived at the market-place, she had three dozen still to sell, how was this possible, without breaking any of the eggs?

Solution.—The possibility of this problem will be evident when it is considered, that by taking the greater half of an odd number, we take the exact half—½. It will he found therefore, that the woman, before she passed the last guard, had 73 eggs remaining, for by selling 37 of them at that guard which is the half—½, she would have 36 remaining. In the like manner, before she came to the second guards she had 147; and before she came to the first, 295.

Two Greeks dicing together, one provided five dishes, the other three. A stranger happened to pop in, and requested to join them. On his departure, he gave the Greek who had provided five dishes five shillings, and to the other who had furnished three dishes, three shillings; but the latter was dissatisfied, and had the matter referred to Solon, who instantly decided that the Greek who had provided five dishes should have seven shillings, and he who furnished the three dishes should receive but one shilling.

Solution.—Each Greek paid eight shillings, which are twenty-four shillings for eight dishes, or three shillings per dish. The one who provided five being fifteen shillings out of pocket, had a right to have seven shillings refunded to him, which left him eight shillings, his proportion.

When first the marriage knot was tied, betwixt my love and me,
My age did then her’s exceed us three times three doth three.
But when we ten and half ten years we man and wife had been,
Her age came up as near to mine, as eight is to sixteen.

Solution.—The man was 45, the woman was 15.