Ponder^this = ponder...

IBM Ponder This #127 · November 2008

Ponder-this corner reached its 127th month, which is the maximal number that fits into signed byte. To celebrate this, we will praise you--our devoted solvers--share some of your flattering emails, and, of course, give you a special ponder-this question.

First, a salute to your persistence. Here's an example of one devoted follower who sent in solutions from the Intensive Care Unit:

"Let me just take this time to thank you and IBM for this wonderful web site. It has provided me with many hours of puzzle solving pleasure, and also some interesting conversations with my family.

The first three weeks of June this year I spent in the hospital. One of the nights in the ICU my family and I passed some of the time by talking about Ponder This. My daughter read the DNA problem to me at that time, and jokingly I told her I could be the first person to ever solve and answer a Ponder This while in the ICU. I actually sent my entry from my hospital bed about a week later.

Again thanks. Looking forward to next month's puzzle."

Many thanks to all of those who sent in great original and innovative riddles.

Of course it is heartwarming to get compliments like:

*"PS.: Thank you 10^10 times for maintaining this extremely enlightening challenge. Each time I participate, I discover a new world.

That's just great! ;-)"*

Lastly, we are proud to tell you about a scientific paper that one of our solvers published a year ago in the prestigious Physics Review Letter journal. The paper was inspired by April 2007's ponder-this puzzle.

ANTENEODO, C.; MORGADO, W.A.M. Critical scaling in standard biased random walks. Physical Review Letters 99(18): 180602-1-4 (2007):

"We acknowledge Brazilian agencies CNPq and Faperj for partial financial support and IBM research "Ponder This" for having drawn attention to this model."

November's puzzle is about replacing digits (0-9) with letters (ponderthis) where each letter represents a different digit. For example, the only solution for the problem

phd*pride + theorist + einstein 
               =
sir*idiot + hedonist + ronnie

670*63905 + 17523941 + 59841598  
         = 120,181,889 =  
493*90921 + 75028941 + 328895

Furthermore, in this case, ponder=628053 and this=1794.

Now for our puzzle. If

${ponder}^{this} = ponder \dots$

I.e., the result of raising the 6-digits number "ponder" to the power of the 4-digit number "this" starts with the six most significant digits of "ponder", then what is the value (translated back to letters) of the first four digits of the following expression?

|.dr-.psi+.norton|      |.ret-.en+.pier|
-----------------   +   ----------------
  .poor\*.heron       .distorted\*.terrier

Note the decimal points: .dr = 0.dr = (10*d+r)/100; and the absolute value signs (|).

Note that "ponder" and "this" should be six and four digits numbers respectively; i.e. "p" and "t" should not be zero.

Solution

Best opened after a real attempt

To be added.

IBM Ponder This #127 · November 2008 ​

IBM Ponder This #127 · November 2008