## Challenge 250: Providing for Pigs

A farmer has 46 pigs and 10 spacious shelters for them to use.

(i) Is it possible for the pigs to go into the shelters so that each shelter contains a different number of pigs? Justify your answer.

In an unfortunate incident involving a wolf, one of the shelters is blown down. (All the pigs are safe, thank goodness!)

(ii) Can the pigs go into the shelters so that each shelter contains a different number of pigs now? What is the largest number of pigs that there could be in the fullest shelter? What is the smallest?

The farmer acquires some more pigs.

(iii) If the smallest possible number of pigs in the fullest of the nine remaining shelters is 12, what is the largest possible number of pigs in the fullest shelter? Can you generalise?

*Based on an original problem by Phoebe (Y13)*