Diamond Dilemma

Algebra Level 3

The diamond symbol is an operation that represents a function that will take the given numbers and will have an output. Study the pattern and find the value that will represent the unknown.

( 1 ⧫ 2 ) = 3 \left( 1\blacklozenge 2 \right) =3

( 3 ⧫ 4 ) = 145 \left( 3\blacklozenge 4 \right) =145

( 5 ⧫ 6 ) = 23 , 401 \left( 5\blacklozenge 6 \right) =23,401

( 7 ⧫ 8 ) = 7 , 861 , 953 \left( 7\blacklozenge 8 \right) =7,861,953

( 9 ⧫ 10 ) = ? \left( 9\blacklozenge 10 \right) =?


The answer is 4486784401.

Gian Alix by Gian Alix , 34, Canada

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1 solution

Gian Alix
Mar 29, 2014

The diamond operation will have this function: ( a ⧫ b ) = a b + b a \left( a\blacklozenge b \right) ={ a }^{ b }+{ b }^{ a }

So, ( 9 ⧫ 10 ) = 9 10 + 10 9 = 4 , 486 , 784 , 401 \left( 9\blacklozenge 10 \right) ={ 9 }^{ 10 }+{ 10 }^{ 9 }=4,486,784,401

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