Polynomials And Factorials

n ! = 9 × 9 × 9 9 \large n! = 9\times9\times9 - 9

What is the value of n n ?

4 5 6 7

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2 solutions

Ben Champion
Mar 19, 2016

An extremely roundabout way of doing it (if you have a lot of time and using a calculator/doing a bunch of multiplication sounds boring):

9 × 9 × 9 9 9 \times 9 \times 9-9

do some factoring:

9 ( ( 3 × 3 ) 2 1 ) 9((3 \times 3)^2-1)

( 9 ) ( ( 3 × 3 ) + 1 ) ( ( ( 3 × 3 ) 1 ) ) (9)((3 \times 3)+1)(((3 \times 3)-1))

( 9 ) ( 10 ) ( 8 ) (9)(10)(8)

( 3 × 3 ) × ( 2 × 5 ) × ( 2 × 2 × 2 ) (3 \times 3) \times (2 \times 5) \times (2 \times 2 \times 2)

which can be rearranged or multiplied out as

1 × 2 × 3 × 4 × 5 × 6 1 \times 2 \times 3 \times 4 \times 5 \times 6

Hahah! This is nice too! Thank you

Chung Kevin - 5 years, 2 months ago

By BODMAS, n ! = 720 n!=720 or n = 6 n=6

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