A problem by Budi Utomo

Level pending

Assumtion that s and t are maximum integers so that 400! divided by 7^s and ((3!)!)! divided by 3^t. value of s + t ?

356 422 380 66

Budi Utomo by Budi Utomo , 23, Indonesia

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1 solution

Budi Utomo
Dec 18, 2013

s --------> |400/7| + |400/49| + |400/343| = 57 + 8 + 1 = 66 t ---------> |720/3| + |720/9| +|720/27| + |720/81 + |720/243| = 240 + 80 + 26 + 8 + 2 = 356

So, s + t = 66 + 356 = 422

0 Helpful 0 Interesting 0 Brilliant 0 Confused

I did it the same way. Those things are floors. But 720 = ( 3 ! ) ! 720=(3!)! . 720 ! 720! would have been out of my range of my calculator. I used the same principle to find out how many zeroes has n ! n! .

Adrian Neacșu - 7 years, 2 months ago

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