Ackermann, who?

Probability Level 2

What is the value of a[3,4}?

a : ( m , n ) → { n + 1 m = 0 a ( m − 1 , 1 ) m > 0 ∧ n = 0 a ( m − 1 , a ( m , n − 1 ) ) True a: (m,n)\to \begin{array}{ll} \{ & \begin{array}{ll} n+1 & m=0 \\ a(m-1,1) & m>0\land n=0 \\ a(m-1,a(m,n-1)) & \text{True} \\ \end{array} \\ \end{array}


The answer is 125.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Table [ a ( i , j ) , { i , 0 , 3 } , { j , 0 , 4 } ] ⇒ ( 1 2 3 4 5 2 3 4 5 6 3 5 7 9 11 5 13 29 61 125 ) \text{Table}[a(i,j),\{i,0,3\},\{j,0,4\}] \Rightarrow \left( \begin{array}{rrrrr} 1 & 2 & 3 & 4 & 5 \\ 2 & 3 & 4 & 5 & 6 \\ 3 & 5 & 7 & 9 & 11 \\ 5 & 13 & 29 & 61 & 125 \\ \end{array} \right)

You really do not want to try to evaluate a(4,2) as that value is 2 65536 − 3 2^{65536}-3 .

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Table is a Wolfram Mathematica function which evaluates the first argument for each cell of a table (matrix) in row major form (i.e., in this case i varies from 0 to 4 across each row and then j varies from 0 to 3 column-wise.

Table

A Former Brilliant Member - 1 year, 11 months ago

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