N000ughty Thoughts

How many noughts are at the end of these giant numbers?

Factorial

How many zeros are there at the end of the number which is the product of first hundred positive integers?

Fac-finding

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.

Squaresearch

Age 14 to 16Challenge Level

Consider numbers of the form $u_n = 1! + 2! + 3! +...+n!$.

How many such numbers are perfect squares?