Solution to the Problem:
The man will need at least 112 coins, giving each child 16
coins in these combinations:
(1) 3 quarters, 3 nickels, 10 pennies;
(2) 2 quarters, 4 dimes, 10 pennies;
(3) 2 quarters, 9 nickels, 5 pennies;
(4) 1 quarter, 4 dimes, 6 nickels, 5 pennies;
(5) 1 quarter, 15 nickels;
(6) 8 dimes, 3 nickels, 5 pennies;
(7) 4 dimes, 12 nickels.