Mathematical game: how old is the captain?

“Since you do geometry and trigonometry, I’m going to give you a problem: a ship is at sea. It left Boston loaded with cottonhe gauges 200 barrels, he sailed for Le Havre; the mainmast is broken, there is a moss on the forecastle; the passengers are twelve in number; the wind breath N.-E.-E. ; the clock strikes a quarter past three in the afternoon; we are in May… We ask captain’s age. »

Here is a riddle of the same style which can however be solved:

The age of the children

To get rid of an intruder who has just approached him, a woman warns him: ” I am married and a mother of four children… “.

The man answered strangely: What are the product and the sum of their ages? »

Taken aback, after a quick mental calculationthe woman answered: 126 and the sum is precisely the number of the house opposite! »

The man thought for a moment before replying: “I can’t find their ages. »

The woman, caught up in the game: “The smaller don’t speak yet. »

Man: “Now I know. »

Question: what are the ages of the four children?

Answer

1, 2, 3 and 21. There are eleven decompositions of 126 into the product of four factors a, b, c and d. Here is the table with the sums S.

The man knows the sum (the house number) but cannot conclude. The sum is therefore equal to 27, which corresponds to two decompositions. One of the cases corresponds to two twins as “youngest”, so the answer is the other.