How many noughts are at the end of these giant numbers?
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.
How many zeros are there at the end of the number which is the product of first hundred positive integers?