IBM Research | Ponder This | November 2006 challenges

# Ponder This

## November 2006

<<October November December>>

Ponder This Challenge:

Puzzle for November 2006.

Consider arithmetic expressions formed from the integers 1,2,3,4 (each of which is to used exactly once) and the operators +,-,* (addition, subtraction, multiplication). We will ask about the values that can be represented by such expressions. For example 1 = (2*3)-(4+1) so 1 can represented. Note 1 = (2+3)-4 would not be a valid representation because it does not use 1.

For this month's puzzle we ask two questions:

1. What is the smallest positive integer that can not be represented by such expressions involving 1,2,3,4.
2. Find a set of 4 distinct positive integers a,b,c,d such that the smallest positive integer that can not be represented by such expressions involving a,b,c,d (instead of 1,2,3,4) is greater than the answer to part 1. You may wish to use a computer for this part.

Revised, 11/3/06, 11:30AM ET: You are allowed to reuse operators (1+2+3+4). You are not allowed to join digits together (12+34). / (divide) is not one of the allowed operators.

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: 11/02/2006 @ 12:00 PM EST
Solution: 12/01/2006 @ 11:00 AM EST
List Updated: 12/05/2006 @ 08:30 AM EST

Eugene Vasilchenko (11.02.2006 @01:14:48 PM EST)
Stephen Steffes (11.02.2006 @01:17:50 PM EST)
Dave Blackston (11.02.2006 @01:23:42 PM EST)
V. Balakrishnan (11.02.2006 @01:26:23 PM EST)
Roberto Tauraso (11.02.2006 @02:27:55 PM EST)
David Friedman (11.02.2006 @02:54:31 PM EST)
Mohammed Ajmal (11.02.2006 @03:50:50 PM EST)
Arthur Breitman (11.02.2006 @03:55:31 PM EST)
Fýrat Solðun (11/02/2006 04:57:40 PM EST)
Jan Rubak (11.02.2006 @05:29:34 PM EST)
Tom Sirgedas (11.02.2006 @05:45:56 PM EST)
Robin Ryder (11.02.2006 @06:00:44 PM EST)
Lawrence Hon (11.02.2006 @07:04:21 PM EST)
Gary M Gerkin (11.02.2006 @08:59:45 PM EST)
John T. Robinson (11.02.2006 @09:54:14 PM EST)
Oleg Trott (11.02.2006 @09:55:43 PM EST)
Gareth McCaughan (11.02.2006 @07:43:10 PM EST)
Matthew Samuel (11.02.2006 @11:01:06 PM EST)
Alvaro Martinez Echevarria (11.02.2006 @11:08:52 PM EST)
Zhou Guang (11.03.2006 @01:42:41 AM EST)
Ariel Flat (11.03.2006 @03:11:01 AM EST)
Satyanarayan Pangigrahi (11.03.2006 @04:31:07 AM EST)
Magnus Bjork (11.03.2006 @05:50:37 AM EST)
Ben North (11.03.2006 @06:36:00 AM EST)
Roger D Thompson (11.03.2006 @07:37:57 AM EST)
Jens Voz (11.03.2006 @09:35:29 AM EST)
Al Zimmermann (11.03.2006 @09:52:58 AM EST)
Alan Murray (11.03.2006 @11:02:10 AM EST)
Gale Greenlee (11.03.2006 @12:21:12 PM EST)
Jack Kennedy (11.03.2006 @01:17:32 PM EST)
John Tromp (11.03.2006 @02:55:32 PM EST)
Vernon W. Miller (11.03.2006 @04:11:14 PM EST)
Justin T Miller (11.03.2006 @04:45:57 PM EST)
Matthew Reeder (11.03.2006 @05:04:15 PM EST)
KjSlag (11.03.2006 @05:16:14 PM EST)
Yurun Liu (11.03.2006 @06:53:14 PM EST)
Torsten Fischer (11.03.2006 @07:29:22 PM EST)
John Dalbec (11.03.2006 @08:28:29 PM EST)
John Roy (11.03.2006 @09:00:35 PM EST)
Anatoly Morosov (11.03.2006 @09:25:46 PM EST)
James Dow Allen (11.03.2006 @11:06:12 PM EST)
Leo Broukhis (11.03.2006 @11:24:41 PM EST)
Sandeep Rathour (11.04.2006 @03:28:54 AM EST)
Christian Blatter (11.04.2006 @03:45:48 AM EST)
Oded Margalit (11.04.2006 @08:31:15 AM EST)
D. Adrian Tanner (11.04.2006 @10:25:07 AM EST)
Vladimir Sedach (11.04.2006 @11:27:30 AM EST)
Rick Kaye (11.04.2006 @12:42:43 PM EST)
Daniel Bitin (11.04.2006 @01:34:55 PM EST)
Benjamin Lee Smith (11.04.2006 @04:32:23 PM EST)
Marcos (11.04.2006 @05:27:18 PM EST)
Roy (11.04.2006 @05:57:33 PM EST)
yooari (11.04.2006 @06:13:38 PM EST)
David W. Cantrell (11.05.2006 @08:36:28 AM EST)
Arjun Archarya (11.05.2006 @09:11:09 AM EST)
Amos Guler (11.05.2006 @09:57:06 AM EST)
Piros Lucian (11.05.2006 @12:51:27 PM EST)
Chris Hills (11.05.2006 @03:25:00 PM EST)
John Ritson (11.05.2006 @06:06:32 PM EST)
Tom Gutman (11.05.2006 @07:37:12 PM EST)
Diego Erdody (11.05.2006 @09:54:47 PM EST)
Ashish Srivastava (11.05.2006 @10:27:13 PM EST)
Jesse Blosser (11.05.2006 @11:04:43 PM EST)
Serge Gautier (11.06.2006 @03:05:12 AM EST)
Edgar Hassler (11.06.2006 @03:35:52 AM EST)
Pirata Somniculosus (11.06.2006 @03:39:15 AM EST)
Chris Hiszpanski (11.06.2006 07:26:35 AM EST)
Amit Elzari (11.06.2006 @08:38:22 AM EST)
Ionel Santa (11.06.2006 @09:30:58 AM EST)
Jarrod Chambers (11.06.2006 @10:02:58 AM EST)
Frank Yang (11.06.2006 @10:18:57 AM EST)
Fabio Filatrella (11.06.2006 @11:07:11 AM EST)
John G. Fletcher (11.06.2006 @11:57:53 AM EST)
Joe Vanore (11.06.2006 @12:14:46 PM EST)
Phil Muhn (11.06.2006 @01:41:01 PM EST)
Joseph DiVincentis (11.06.2006 01:57:26 PM EST)
Jamie Broomall (11.06.2006 @04:44:30 PM EST)
Todd Harris (11.06.2006 @06:55:16 PM EST)
John Stebbins (11.06.2006 @10:56:08 PM EST)
Greg Janoe (11.07.2006 @12:40:10 AM EST)
David McQuillan (11.07.2006 @04:08:55 AM EST)
Alan O'Donnell (11.07.2006 @09:20:41 AM EST)
Muralidhar Seshadri (11.07.2006 @10:00:54 AM EST)
Emmanuel Candalh (11.07.2006 @10:52:08 AM EST)
David Norman (11.07.2006 @12:46:12 PM EST)
Dan McGrath (11.07.2006 @04:22:17 PM EST)
Hagen von Eitzen (11.07.2006 @04:28:46 PM EST)
Wolfgang Kais (11.07.2006 @06:15:30 PM EST)
Robert Szafranski (11.07.2006 @06:17:11 PM EST)
Didier Bizzarri (11.07.2006 @07:46:28 PM EST)
Mark J Murphy (11.08.2006 @03:28:30 AM EST)
Nyles Heise (11.08.2006 @03:41:36 AM EST)
Daniel Chong Jyh Tar (11.08.2006 @06:41:40 AM EST)
Clive Tong (11.08.2006 @07:06:33 AM EST)
Krunoslav Kovac (11.08.2006 @06:33:56 PM EST)
Ed Sheppard (11.08.2006 @07:07:12 PM EST)
Chuck Carroll (11.08.2006 @08:27:49 PM EST)
Shubin Hu (11.08.2006 @10:59:15 PM EST)
Dion K Harmon (11.09.2006 @02:41:07 AM EST)
Amin Allam (11.09.2006 @10:03:17 AM EST)
Marcin Mauk (11.09.2006 @12:43:15 PM EST)
Fred Bone (11.09.2006 @02:47:15 PM EST)
Chris Shannon (11.09.2006 @03:24:01 PM EST)
Mark Perkins (11.09.2006 @06:07:24 PM EST)
Jason Horowitz (11.09.2006 @09:24:49 PM EST)
Tim MacDonald (11.09.2006 @10:24:41 PM EST)
Tran Duc Hieu (11.10.2006 @08:34:16 AM EST)
Rune Fevang (11.10.2006 @10:05:14 PM EST)
Wu Mingrui (11.11.2006 @03:04:46 PM EST)
Zhang Qilin (11.11.2006 @08:04:13 PM EST)
Claudio Baiocchi (11.12.2006 @09:34:53 AM EST)
Laszlo Kozma (11.12.2006 @04:36:13 PM EST)
Shmuel Menachem Spiegel (11.12.2006 @04:39:29 PM EST)
Shankar Ananthanarayanan (11.13.2006 @06:35:17 AM EST)
Riyaaz Shaik (11.13.2006 @07:47:50 AM EST)
Sunil Srivastava (11.13.2006 @06:16:47 PM EST)
Arunkumar Muralidharan (11.13.2006 @06:23:50 PM EST)
Dave Gower (11.13.2006 @06:27:43 PM EST)
Christopher Howe (11.13.2006 @11:25:58 PM EST)
Emilio Schiavi (11.14.2006 @03:32:18 AM EST)
Raghavendra G Reddy (11.14.2006 @08:27:41 AM EST)
John Hubenschmidt (11.14.2006 @01:52:49 PM EST)
Antonio Manuel Gutierrez Fernandez (11.14.2006 @02:16:52 PM EST)
Albert Mao (11.14.2006 @11:31:18 PM EST)
Ray Gregory (11.14.2006 @11:31:58 PM EST)
Are Hjørungnes (11.15.2006 @03:53:18 AM EST)
Richard Mann (11.15.2006 @05:39:25 AM EST)
Harold Gutch (11.15.2006 @06:05:00 AM EST)
Lukasz Bolikowski (11.15.2006 @08:02:38 AM EST)
Keith Wilcock (11.15.2006 @10:43:53 AM EST)
Johannes Schindelin (11.15.2006 @02:38:44 PM EST)
Raghu Adari (11.16.2006 @12:07:17 AM EST)
Sridivakar Inakonda (11.16.2006 @12:14:01 AM EST)
Joel Bleuse (11.16.2006 @07:20:54 AM EST)
Steven Lambert (11.16.2006 @12:44:42 PM EST)
Marty Gilligan (11.16.2006 @07:34:56 PM EST)
Segher Boessenkool (11.17.2006 @08:54:00 AM EST)
Bengu Li (11.17.2006 @02:39:23 PM EST)
Wolf Mosle (11.19.2006 @11:51:53 AM EST)
David Cleaver (11.19.2006 @01:52:39 PM EST)
Wexp2 (11.20.2006 @01:36:08 AM EST)
Hai Duong (11.20.2006 @03:26:34 AM EST)
Ananda Raidu (11.20.2006 @06:56:31 AM EST)
Mario Roederer (11.20.2006 @08:53:27 AM EST)
Stephen Boudreaux (11.21.2006 @01:07:33 AM EST)
Eddie Marcus (11.21.2006 @10:05:19 PM EST)
David O'Hagan (11.22.2006 @12:54:50 AM EST)
Charles A. Barrow (11.22.2006 @09:10:57 AM EST)
Reinder Verlinde (11.22.2006 @11:21:20 AM EST)
Ashutosh Mahajan (11.23.2006 @02:10:42 AM EST)
Adrian Atanasiu (11.23.2006 @06:53:38 AM EST)
Vivek Nema (11.23.2006 @06:02:47 PM EST)
Adriana Clerci (11.24.2006 @01:29:57 PM EST)
Narayanan Rajamani (11.24.2006 @04:34:04 PM EST)
Vance (11.26.2006 @12:26:05 AM EST)
Edna Mantsour (11.26.2006 @01:07:16 PM EST)
Allen Wan (11.27.2006 @01:49:17 AM EST)
Bradley Wild (11.27.2006 @01:11:16 PM EST)
Adrian Groves (11.28.2006 @07:09:00 AM EST)
Anatoly Lushev (11.30.2006 @01:42:03 PM EST)
Michael Chirozzi (11.30.2006 @05:28:04 PM EST)
Stephen Lesko (12.01.2006 @09:09:36 AM EST)

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