Four men who had a monkey bought a pile of mangoes. At night one of the men came to the pile of mangoes while the others slept and, finding that there was just one more mango than could be exactly divided by four, he tossed the extra mango to the monkey and took away one fourth of the remainder. Then he went back to sleep.

Presently another of them awoke and went to the pile of mangoes. He also found just one too many to be divided by four so he tossed the extra one to the monkey, took one fourth of the remainder, and returned to sleep.

After a while the third rose also, and he too gave one mango to the monkey and took away the whole number of mangoes which represented precisely one fourth of the rest.

Lastly, the fourth man woke up and he also found one extra mango when he divided the mangoes that he found into four. So he threw the extra one to the monkey and took away one fourth of the mangoes that he found.

Next morning the four men got up and went to the pile. Again they found just one too many, so they gave one to the monkey and divided the rest evenly. What is the least number of mangoes with which this can be done? Formulate this problem as an integer programming model.

What is the decision variable?

What is the objective function?

What are the constraints?