An eccentric sheikh left a will to distribute a herd of camels among his three children:

Tarek receives at least one-half of the herd, Sharif gets at least one third, and Maisa gets at least one-seventh. The remainder goes to charity. The will does not specify the size of the herd except to say that it is an odd number of camels and that the named charity receives exactly one camel. Use ILP to determine how many camels the sheikh left in the estate and how many each child got.