Permutated Pooled Pascal (Power of 8)

Algebra Level 3

( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 ) 1 + 8 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) 2 + 28 ( 1 + 2 + 3 + 4 + 5 + 6 ) 3 + 56 ( 1 + 2 + 3 + 4 + 5 ) 4 + 70 ( 1 + 2 + 3 + 4 ) 5 + 56 ( 1 + 2 + 3 ) 6 + 28 ( 1 + 2 ) 7 + 8 ( 1 ) 8 = ? \begin{aligned} && { (1+2+3+4+5+6+7+8) }^{ 1 } \\ & +& 8 { (1+2+3+4+5+6+7) }^{ 2 } \\ & +&28{ (1+2+3+4+5+6) }^{ 3 } \\ & +&56{ (1+2+3+4+5) }^{ 4 } \\ & +&70{ (1+2+3+4) }^{ 5 } \\ & +&56{ (1+2+3) }^{ 6 } \\ & +&28 { (1+2) }^{ 7 } \\ & +&8 { (1) }^{ 8 } \\ & =& \ ? \end{aligned}


The answer is 12774596.

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1 solution

Krishna Shankar
Apr 12, 2015

By adding the values 36+6272+259308+2835000+7*10^6+2612736+61236+8=12774596

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