SOLUTION: Find some value R, {{{R!/((R-3)!(R-4)!)=1}}}. Find the sum of the digits of R. R! over (R-3)!(R-4)! = 1

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Question 1152304: Find some value R, R%21%2F%28%28R-3%29%21%28R-4%29%21%29=1. Find the sum of the digits of R.
R! over (R-3)!(R-4)! = 1
Found 2 solutions by math_helper, Edwin McCravy:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
R!/((R-3)!(R-4)!) = 1

Using trial and error...
8!/(5!*4!) = 8*7*6/(4!) = 336/24 > 1
9!/(6!*5!) = 9*8*7/(5!) = 504/120 > 1
10!/(7!*6!) = 10*9*8/(6!) = 720 / 720 = 1

So R = 10 satisifies the equation.
The sum of the digits of R is equal to +highlight%28+1+%29+


Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
                   
R%21%2F%28%28R-3%29%21%28R-4%29%21%29=1

R has to be 4 or more, so we start trying to find R, so we will get 1

4%21%2F%28%284-3%29%21%284-4%29%21%29=4%21%2F%281%210%21%29=24%2F%281%2A1%29=24

5%21%2F%28%285-3%29%21%285-4%29%21%29=5%21%2F%282%211%21%29=120%2F%282%2A1%29=60

6%21%2F%28%286-3%29%21%286-4%29%21%29=6%21%2F%283%212%21%29=720%2F%286%2A2%29=60

7%21%2F%28%287-3%29%21%287-4%29%21%29=7%21%2F%284%213%21%29=120%2F%2824%2A6%29=35

8%21%2F%28%288-3%29%21%288-4%29%21%29=8%21%2F%285%214%21%29=40320%2F%28120%2A24%29=14

9%21%2F%28%289-3%29%21%289-4%29%21%29=9%21%2F%286%215%21%29=362880%2F%28720%2A120%29=4.2

10%21%2F%28%2810-3%29%21%2810-4%29%21%29=10%21%2F%287%216%21%29=3628800%2F%285040%2A720%29=1

Finally found it!  R=10

The sum of the digits of 10 is 1+0 = 1

Edwin