IBM Research | Ponder This | November 2010 challenges

# Ponder This

## November 2010

<<October November December>>

Ponder This Challenge:

November's challenge is dedicated to IBM Fellow Benoît Mandelbrot, who died on October 14, 2010, at the age of 85.

Let's define a function f on five variables (i, j, k, l, and m) as follows:

If (i-m)*(j-m) is zero then
f(i,j,k,l,m) ← ((abs(j-(1-k+l)*m)-m+1)* (abs(i-(k+l)*m)-m+1))
else
f(i,j,k,l,m) ← f(i mod m,
j mod m,
int(((i^j)&((m*l)^i))/m)^l^k^int(i/m),
int(((i^j)&((m*k)^i))/m)^l,
m/2)

Where
x^y      means bitwise xor (exclusive or)
x&y     means bitwise and (conjunction)
abs    is the absolute value
mod   is the modulo function
int       means truncating downwards to an integer

What should be the input to the function f, and how do you need to interpret its output to associate it with Professor Mandelbrot?

Update: November 5th: We are *not* looking for his age.

Update: December 1st: m is a power of 2.

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Challenge: 11/02/2010 @ 10:30 AM EST
Solution:
List Updated: 11/02/2010 @ 10:30 AM EST

### People who answered correctly:

Mark Mixer (11/02/2010 08:32 PM EDT)
John Tromp (11/02/2010 11:50 PM EDT)
John T. Robinson (11/11/2010 03:16 PM EDT)
Sylvain Becker (11/11/2010 08:22 PM EDT)
Piet Orye (11/15/2010 10:34 AM EDT)
Tim Tran (12/05/2010 04:31 AM EDT)
Luke Pebody (12/06/2010 04:00 PM EDT)

Attention: If your name is posted here and you wish it removed please send email to the ponder@il.ibm.com.