Factorials

problem
Favourite

Fac-Finding

Age

14 to 16

Challenge level

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.
problem

How Does Your Function Grow?

Age

16 to 18

Challenge level

Compares the size of functions f(n) for large values of n.
problem

Growing

Age

16 to 18

Challenge level

Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)
problem

Squaresearch

Age

14 to 16

Challenge level

Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
problem

Forgotten Number

Age

11 to 14

Challenge level

I have forgotten the number of the combination of the lock on my briefcase. I did have a method for remembering it...
problem

Factoring Factorials

Age

11 to 14

Challenge level

Find the highest power of 11 that will divide into 1000! exactly.
problem

Powerful Factorial

Age

11 to 14

Challenge level

6! = 6 × 5 × 4 × 3 × 2 × 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4) = 45. What is the highest power of two that divides exactly into 100!?
problem

Trailing Zeros

Age

11 to 14

Challenge level

How many zeros does 50! have at the end?
problem

N000ughty

Age

14 to 16

Challenge level

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

Factorial

Age

14 to 16

Challenge level

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