Riddle:

The head of a tribe has 20 kilos of maize to distribute to its 20 neighbors and decide to do as follows :

• Each of the children he gives 3 kilos of maize.
• Each of the women given two kilos of maize.
• Each of the men given half a kilo of corn.

Knowing that at least there is a child , a woman and a man who handed out all uneaten or corn without missing anything How many children , women and men are there?

Solution:

For the wording of the puzzle we know that the lower limits are a child , a woman and a man, we will seek the maximum limits.

The upper limit on the number of children is 5, if more corn would have missed.

The upper limit on the number of women is 8 for the same reason.

The upper limit on the number of men is much higher, 18 men to have at least one woman and a child to be a total of 20 residents.

With these maximum in each group we have these combinations:

 Children Women Men 1 1 18 2 1 17 3 1 16 4 1 15 5 1 14 1 2 17 2 2 16 3 2 15 4 2 14 5 2 13 1 3 16 2 3 15 3 3 14 4 3 13 5 3 12 1 4 15 2 4 14 3 4 13 4 4 12 5 4 11 1 5 14 2 5 13 3 5 12 4 5 11 5 5 10 1 6 13 2 6 12 3 6 11 4 6 10 5 6 9 1 7 12 2 7 11 3 7 10 4 7 9 5 7 8 1 8 11 2 8 10 3 8 9 4 8 8 5 8 7

From the above table odd numbers retired men by preventing the division the result is integer, we put next to each row kilos of corn would correspond to each group and the total sum:

 Children Women Men KG Children KG Women KG Men TOTAL 1 1 18 3 2 9 14 3 1 16 9 2 8 19 5 1 14 15 2 7 24 2 2 16 6 4 8 18 4 2 14 12 4 7 23 1 3 16 3 6 8 17 3 3 14 9 6 7 22 5 3 12 15 6 6 27 2 4 14 6 8 7 21 4 4 12 12 8 6 26 1 5 14 3 10 7 20 3 5 12 9 10 6 25 5 5 10 15 10 5 30 2 6 12 6 12 6 24 4 6 10 12 12 5 29 1 7 12 3 14 6 23 3 7 10 9 14 5 28 5 7 8 15 14 4 33 2 8 10 6 16 5 27 4 8 8 12 16 4 32

The solution to the math puzzle for the old account is 1 child, 5 women and 14 men. Would you know do it riding an equation?