Simple as that

Consider three natural numbers n 1 , n 2 , n 3 n_{1} ,n_{2}, n_{3} defined as

n 1 = x 1 x 2 x 3 x 4 - n_{1`}=x_{1}x_{2}x_{3}x_{4} ( 4 d i g i t n u m b e r 4~digit~number )

n 2 = y 1 y 2 y 3 - n_{2}=y_{1}y_{2}y_{3} ( 3 d i g i t n u m b e r 3~digit~number )

n 3 = z 1 z 2 - n_{3}=z_{1}z_{2} ( 2 d i g i t n u m b e r 2~digit~number )

where x 1 . . . . x 4 , y 1 . . . y 3 , z 1 , z 2 x_{1}....x_{4},y_{1}...y_{3},z_{1},z_{2} are all non zero digits .

Then total number of nine digit numbers formed by picking up the digits used in the numbers n 1 , n 2 , n 3 n_{1},n_{2},n_{3} if digits are taken only from the right side of either of the numbers n 1 , n 2 a n d n 3 n_{1},n_{2}~and~n_{3}


The answer is 1260.

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1 solution

Tanishq Varshney
Mar 18, 2015

its easy u see 9 ! 4 ! × 3 ! × 2 ! \frac{9!}{4!\times 3!\times 2!}

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