Question

A total of 15 pennies are put into four piles so that each pile has a different number of pennies. what is the smallest possible number of pennies that could be in the largest pile

Answer 1

15 pennies are put into 4 piles such that each pile has a different number of penny. The smallest possible number of pennies that could be in the largest pile is 6 because of the only possible arrangement shown in the figure which satisfies the given statement that all piles should have different number of pennies.
In the figure, if the last penny i.e. the 15th penny is placed in the 1 st pile the number would be the same as that of the 2nd pile. Similarly if it is placed in the 2nd pile the number would be same as that of 3rd pile and if placed in the 3rd pile it will be same as the 4th pile. That is the reason why their is one extra penny placed in the 4th pile making it the largest pile with 6 pennies.