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#### Resources tagged with Factorials similar to Black Box:

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### There are 9 results

Broad Topics > Numbers and the Number System > Factorials

### N000ughty Thoughts

##### Stage: 4 Challenge Level:

Factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts? Convince yourself that the above is true. Perhaps your methodology will help you find the. . . .

### Growing

##### Stage: 5 Challenge Level:

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

### Weekly Challenge 36: Seriesly

##### Stage: 5 Short Challenge Level:

Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!

### Factorial

##### Stage: 4 Challenge Level:

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

### Factorial Fun

##### Stage: 5 Challenge Level:

How many divisors does factorial n (n!) have?

### Seriesly

##### Stage: 5 Challenge Level:

Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!

### How Does Your Function Grow?

##### Stage: 5 Challenge Level:

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

### Fac-finding

##### Stage: 4 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.

### The Harmonic Triangle and Pascal's Triangle

##### Stage: 5

The harmonic triangle is built from fractions with unit numerators using a rule very similar to Pascal's triangle.