IBM Research | Ponder This | October 2001 challenges

# Ponder This

## October 2001

<<September October November>>

Ponder This Challenge:

This month's puzzle comes from Laszi Ladanyi, who heard it in college.

Find a function f from R (that is, the set of real numbers) to R
such that for all open intervals I=(u,v) ,we have that f maps (u,v) onto R.
The function f is independent of u,v.

(That is, given any target real number t, and any interval
I=(u,v) with u<v, there is x with u<x<v and f(x)=t.)

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

Challenge: 10/01/2001 @ 10:30 AM EST
Solution: 10/31/2001 @ 10:30 AM EST
List Updated: 10/31/2001 @ 10:30 AM EST

### People who answered correctly:

Bill Roscoe (10.01.2001 @ 11:35 AM EDT)
Henry Bottomley (10.01.2001 @ 12:22 PM EDT)
Vineet Gupta (10.01.2001 @ 2:56 PM EDT)
George Ross (10.02.2001 @ 2:35 PM EDT)
Alexey Vorobyov (10.02.2001 @ 2:51 PM EDT)
Ionel Santa (10.03.2001 @ 2:39 AM EDT)
Jacques Willekens (10.03.2001 @ 3:13 AM EDT)
Vadim Alexandrov (10.03.2001 @ 8:40 AM EDT)
James McGrath (10.03.2001 @ 2:40 PM EDT)
Marian Olteanu (10.04.2001 @ 3:52 PM EDT)
Ruth Algor (10.03.2001 @ 8:46 PM EDT)
Andreas Spillner (10.04.2001 @ 4:07 AM EDT)
Hilary Jones (10.04.2001 @ 9:54 PM EDT)
Ben North (10.05.2001 @ 10:49 AM EDT)
Andy Lowry & Howie Kaye (10.05.2001 @ 11:44 AM EDT)
Vladimir Sedach (10.05.2001 @ 3:35 PM EDT)
Sameer Udeshi (10.05.2001 @ 3:52 PM EDT)
Saibal Mitra (10.06.2001 @ 6:26 PM EDT)
Marian Vasile (10.08.2001 @ 10:31 AM EDT)
Felipe Bertrand and Cesar Sanchez (10.09.2001 @ 2:08 PM EDT)
Oleg Mazurov (10.10.2001 @ 1:26 AM EDT)
Jens Voss (10.10.2001 @ 3:47 AM EDT)
David G Radcliffe (10.12.2001 @ 4:05 PM EDT)
Chi-Bong Chan (10.13.2001 @ 3:39 PM EDT)
Ross Millikan (10.15.2001 @ 11:26 AM EDT)
G XU (10.15.2001 @ 1:15 PM EDT)
Victor Chang (10.15.2001 @ 8:22 PM EDT)
Koen Claessen (10.16.2001 @ 4:49 AM EDT)
Christopher Howe (10.17.2001 @ 7:04 PM EDT)
Vishaal Kapoor (10.20.2001 @ 3:45 AM EDT)
John Lamping (10.20.2001 @ 3:04 PM EDT)
Devin Sezer (10.26.2001 @ 8:37 PM EDT)

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