a) King Haggard has a velvet pouch filled with diamonds. He can divide these diamonds into 3 equal piles, 4 equal piles, or 5 equal piles. How many diamonds does he have if it is known that his collection contains less than 100 diamonds in total?
b) King Haggard has a stash of gold coins. He is one coin short of being able to divide these coins into 4 equal piles, or 5 equal piles, or 6 equal piles, or 7 equal piles. How many coins does he have if he has fewer than 500?