Too bad. Can’t be done.

Two odd numbers added together always equals an even number. Four odd numbers added together is simply doing this twice. 15 is an odd number. You can’t get it by adding four odd numbers together, then.

The farmer can create three very small pens and put one pig in each.

Then the farmer can create a large pen, which contains the three small pens inside of it, and put twelve pigs inside the large pen but outside each of the smaller pens.

Then the small pens each contain 1 pig, and the largest pen contains 15 pigs (the 12 pigs outside the three smaller pens, and the 3 pigs inside the smaller pens, which are also inside the large one).

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There’s no way to solve this problem without having some pens contained in another or having pens overlap in some way like this, because the sum of four odd numbers can’t be odd.

Leaving a pen empty won’t work, because then that pen contains 0 pigs, and 0 isn’t an odd number.

he’s going have to buy another pig then

This is impossoible, it may not be done.

When 2 numbers are added they equal an even number. Fourn odd numbers being added is doing it twice. The number 15 is unequal. You cannot get it by adding 4 odd numbers together.