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N000ughty Thoughts

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


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


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.


Age 14 to 16
Challenge Level

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

How many such numbers are perfect squares?