5 times 5

Number Theory Level 2

5 ! − ( 5 − 1 ) ! − ( 5 − 2 ) ! − ( 5 − 3 ) ! − ( 5 − 4 ) ! = ? \large 5! - (5-1)! - (5-2)! - (5-3)!- (5-4)! = \, ?

Notation : ! ! denotes the factorial notation. For example, 8 ! = 1 × 2 × 3 × ⋯ × 8 8! = 1\times2\times3\times\cdots\times8 .

24 25 120 5 87

A Former Brilliant Member by A Former Brilliant Member

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Hung Woei Neoh
Aug 3, 2016

5 ! − ( 5 − 1 ) ! − ( 5 − 2 ) ! − ( 5 − 3 ) ! − ( 5 − 4 ) ! = 5 ! − 4 ! − 3 ! − 2 ! − 1 ! = 5 ( 4 ! ) − 4 ! − 3 ! − 2 ! − 1 ! = 4 ( 4 ! ) − 3 ! − 2 ! − 1 ! = 16 ( 3 ! ) − 3 ! − 2 ! − 1 ! = 15 ( 3 ! ) − 2 ! − 1 ! = 45 ( 2 ! ) − 2 ! − 1 ! = 44 ( 2 ! ) − 1 ! = 88 ( 1 ! ) − 1 ! = 87 ( 1 ! ) = 87 5! - (5-1)!-(5-2)!-(5-3)!-(5-4)!\\ =5!-4!-3!-2!-1!\\ =5(4!)-4!-3!-2!-1!\\ =4(4!)-3!-2!-1!\\ =16(3!)-3!-2!-1!\\ =15(3!)-2!-1!\\ =45(2!)-2!-1!\\ =44(2!)-1!\\ =88(1!)-1!\\ =87(1!)\\ =\boxed{87}

5 Helpful 0 Interesting 0 Brilliant 0 Confused

It's a permutation problem so: 5! + 4! + 3! + 2! + 1! =120 -24 -6 -2 -1 =87

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Typo: 5 ! − 4 ! − 3 ! − 2 ! − 1 ! 5! \color{#D61F06}{-}4!\color{#D61F06}{-}3!\color{#D61F06}{-}2!\color{#D61F06}{-}1!

Hung Woei Neoh - 4 years, 10 months ago
Jesse Nieminen
Aug 17, 2016

5 ! − ( 5 − 1 ) ! − ( 5 − 2 ) ! − ( 5 − 3 ) ! − ( 5 − 4 ) ! = 5 ! − 4 ! − 3 ! − 2 ! − 1 ! = 120 − 24 − 6 − 2 − 1 = 87 5! - (5-1)! - (5-2)! - (5-3)!- (5-4)! = 5! - 4! - 3! - 2! - 1! = 120 - 24 - 6 - 2 - 1 = \boxed{87}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...