IBM Research | Ponder This | November 2004 challenges

# Ponder This

## November 2004

<<October November December>>

Ponder This Challenge:

Puzzle for November 2004

This month's puzzle again comes from IQSTAR.
One or both parts can be solved.

Part 1:
The numbers 1 to 9999 (decimal base) were written on a paper. Then the paper was partially eaten by worms. It happened that just those parts of paper with digit "0" were eaten. Consequently the numbers 1200 and 3450 appear as 12 and 345 respectively, whilst the number 6078 appears as two separate numbers 6 and 78. What is the sum of the numbers appearing on the worm-eaten paper?

Part 2:
Suppose the numbers are represented in the base b system. The digits are 0,1,2,3,...,a, where numerically "a" is equal to b-1. The first b^n-1 numbers, 1 through aaa...a, (that is, the last number is an n-digit number with all its digits
equal to "a") were written on a paper. Then it happened that just those parts of paper with the digits "0", "1", ..., "x-1" were worm-eaten (i.e. the remaining numbers consist of digits belong to {"x", "x+1", ..., "a"}, and suppose 0<x<a). For example, in Part 1 we have b=10, a=9, n=4 and x=1. What is the sum of the numbers appearing on the worm-eaten paper in terms of b, n and x?

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: 11/01/2004 @ 9:00 AM ET
Solution: 12/01/2004 @ 8:30 AM ET
List Updated: 11/01/2004 @ 9:00 AM ET

Part 1
Raicho Tchalkov (11.01.2004 @11:16:18 AM EST)
Daniel Wood (11.01.2004 @12:22:01 PM EST)
Colin Bell (11.01.2004 @01:19:07 PM EST)
Joseph DeVincentis (11.01.2004 @01:44:26 PM EST)
Kalyana Chakravarthys (11.01.2004 @02:30:07 PM EST)
Mike Rousse (11.01.2004 @05:29:50 PM EST)
Trapti Dixit (11.01.2004 @06:47:38 PM EST)
Nirmal Balaraman (11.01.2004 @07:50:04 PM EST)
Vineet Batra (11.02.2004 @01:00:55 AM EST)
Vincent Vermaut (11.02.2004 @02:27:40 AM EST)
Gyora Benedek (11.02.2004 @04:08:02 AM EST)
Satish Vedantam (11.02.2004 @08:58:16 AM EST)
Dan Dima (11.02.2004 @09:14:13 AM EST)
Eugene Vasilchenko (11.02.2004 @10:30:05 AM EST)
Markus Nauroth (11.02.2004 @12:01:19 PM EST)
Ari (11.02.2004 @02:56:08 PM EST)
Radu Grigore (11.02.2004 @03:13:16 PM EST)
Gyozo Nagy (11.02.2004 @03:25:35 PM EST)
Daniel H. Li (11.02.2004 @04:29:53 PM EST)
Naga Thogiti (11.02.2004 @09:25:44 PM EST)
Siva Dirisala (11.02.2004 @09:58:27 PM EST)
Daniel Voina (11.03.2004 @03:59:13 AM EST)
Clive Tong (11.03.2004 @09:51:14 AM EST)
Vineet Dwivedi (11.03.2004 @11:48:28 AM EST)
Shiva P Kasiviswanathan (11.03.2004 @01:54:25 PM EST)
Vinay Mallikarjun Igure (11.03.2004 @03:25:16 PM EST)
Jose H. Nieto (11.03.2004 @05:44:13 PM EST)
Alexis G. Megas (11.03.2004 @06:18:59 PM EST)
Paul Cleary (11.03.2004 @07:58:00 PM EST)
Allan Lazarovici (11.03.2004 @08:23:27 PM EST)
Phil Lazarovici (11.03.2004 @10:10:24 PM EST)
Kim Se Kwon (11.03.2004 @11:52:26 PM EST)
Amit Kumar (11.04.2004 @02:32:45 AM EST)
Vince Lynch (11.04.2004 @10:25:47 AM EST)
Vasudev Nayak (11.04.2004 @12:25:00 PM EST)
Vamsidhar Sunkari (11.04.2004 @01:16:00 PM EST)
Frank Mullin (11.04.2004 @04:56:54 PM EST)
Divyesh Dixit (11.04.2004 @06:07:12 PM EST)
John Konglathu (11.04.2004 @06:19:54 PM EST)
Vamsi Dhar (11.04.2004 @11:07:13 PM EST)
Nikhil Sahasrabudhe (11.05.2004 @11:23:58 AM EST)
Atul Kumar Gupta (11.05.2004 @01:16:51 AM EST)
Dharmadeep Muppalla (11.05.2004 @01:42:33 AM EST)
Troy Lee (11.05.2004 @02:39:14 PM EST)
Gerald Harrison (11.05.2004 @07:29:45 AM EST)
Gaurav Agrawal (11.06.2004 @05:16:51 PM EST)
Bhimasankar Raju Potturi (11.06.2004 @10:45:52 PM EST)
Abishek Kumarasubramanian (11.07.2004 @01:35:07 PM EST)
Paul Botham (11.07.2004 @02:13:47 PM EST)
Princess Melany (11.07.2004 @02:35:50 PM EST)
Indrajit Mukherjee (11.07.2004 @03:48:45 PM EST)
Patrick J. LoPresti (11.07.2004 @08:10:07 PM EST)
Prasanta Babu Jashti (11.08.2004 @05:22:24 AM EST)
Biju Mohan (11.08.2004 @06:22:37 AM EST)
Joseph R Chadwick (11.08.2004 @12:32:50 PM EST)
Yong Liu (11.08.2004 @04:26:19 PM EST)
David Auclair (11.08.2004 @04:28:32 PM EST)
Enrique Velazquez (11.08.2004 @05:03:59 PM EST)
Udhay Kumar (11.09.2004 @12:32:14 AM EST)
Patrick Coleman (11.09.2004 @03:29:00 AM EST)
Prakash Sachania (11.09.2004 @04:40:30 AM EST)
Ajay Reddy Mallepally (11.09.2004 @06:09:57 AM EST)
Rick Sprague (11.09.2004 @02:33:35 PM EST)
Masta Kuno (11.09.2004 @07:25:02 PM EST)
Mark Iuzzolino (11.09.2004 @08:28:41 PM EST)
Samantha Casanova (11.10.2004 @03:59:33 PM EST)
Usman Tahir (11.11.2004 @11:25:27 AM EST)
Praveen Kumar J (11.11.2004 @01:21:00 PM EST)
Joaquim Carrapa (11.11.2004 @03:29:34 PM EST)
John Ritson (11.11.2004 @04:41:53 PM EST)
David Friedman (11.11.2004 @06:41:07 PM EST)
Jeff Shute (11.12.2004 @01:35:31 AM EST)
Michael Brand (11.12.2004 @02:23:01 AM EST)
Daniel Chong Jyh Tar (11.12.2004 @12:53:38 PM EST)
Guler Amos (11.14.2004 @03:01:14 AM EST)
Alexandru Sofronia (11.14.2004 @12:50:51 PM EST)
Richard A Bauer (11.14.2004 @04:03:03 PM EST)
Taku Tamagawa (11.14.2004 @06:09:49 PM EST)
Kennedy (11.15.2004 @01:46:47 AM EST)
Nick Matelli (11.15.2004 @03:04:51 AM EST)
Melvin Carvalho & Andrew Nubbert (11.15.2004 @09:53:00 AM EST)
Chauncey Zheng (11.15.2004 @10:22:42 PM EST)
Thomas Rast (11.16.2004 @04:58:08 PM EST)
Lakshaman Parihar (11.17.2004 @05:44:23 AM EST)
Kalyan Chakravarthy Gudimella (11.17.2004 @08:20:23 AM EST)
David Cavanagh (11.17.2004 @09:55:04 AM EST)
Claudio Baiocchi (11.17.2004 @10:30:13 AM EST)
Scott Miller (11.17.2004 @01:25:00 PM EST)
Wills Accad (11.17.2004 @02:56:20 PM EST)
Chu-Wee Lim (11.17.2004 @04:29:20 PM EST)
Tadej Svetek (11.18.2004 @04:27:07 AM EST)
Max Alekseyev (11.18.2004 @07:26:23 AM EST)
Forrest McClellan (11.18.2004 @04:12:27 PM EST)
George Chen (11.18.2004 @04:37:28 PM EST)
Hari Sethuraman (11.18.2004 @06:11:07 PM EST)
Tang Ming Fai (11.19.2004 @06:08:02 AM EST)
Narayana Babu (11.19.2004 @06:11:18 AM EST)
Alan O'Donnell (11.19.2004 @08:48:19 AM EST)
Krishna Kumar (11.19.2004 @08:59:31 AM EST)
Robin Abraham (11.19.2004 @09:37:56 PM EST)
Alex Skorin (11.21.2004 @10:27:22 AM EST)
Alex Tikhonov (11.21.2004 @01:33:36 AM EST)
Lishchenko Yury (11.21.2004 @03:24:00 AM EST)
Souvik Bose (11.21.2004 @11:40:59 PM EST)
Muharrem Gorkem (11.22.2004 @03:47:56 AM EST)
Owen Wright (11.22.2004 @08:03:39 AM EST)
Logan Ingalls (11.22.2004 @09:06:27 AM EST)
Uday Kale (11.22.2004 @01:00:18 PM EST)
Harsha (11.22.2004 @03:03:36 PM EST)
Raul Guiu (11.22.2004 @08:53:31 PM EST)
Michael Brundage (11.23.2004 @03:35:08 AM EST)
Ashutosh Sodhani (11.23.2004 @03:49:01 AM EST)
Alok Panigrahy (11.23.2004 @05:36:58 AM EST)
Dmitry Chmyr (11.23.2004 @08:32:54 AM EST)
Victor Espigares (11.23.2004 @08:20:35 AM EST)
Dion K Harmon (11.24.2004 @02:57:32 AM EST)
Yuyah (11.24.2004 @04:38:31 AM EST)
Ananda Raidu (11.24.2004 @07:12:37 AM EST)
Franco Bassi (11.24.2004 @05:55:00 PM EST)
Mark Pilloff (11.25.2004 @08:52:27 AM EST)
Jinhong Kim (11.25.2004 @09:38:40 AM EST)
Tony Lin (11.25.2004 @12:43:59 PM EST)
Paul Vandenkeybus (11.26.2004 @06:40:43 AM EST)
Arun (11.26.2004 @07:13:05 AM EST)
John G. Fletcher (11.26.2004 @11:04:18 AM EST)
Rico Blaser (11.26.2004 @11:49:13 AM EST)
Fakrudeen Ali Ahmed (11.26.2004 @01:46:40 AM EST)
Himanshu Dhar (11.26.2004 @02:03:13 PM EST)
Hassan Masum (11.26.2004 @02:52:50 PM EST)
Mark J Murphy (11.27.2004 @09:55:28 PM EST)
Rubén Hernández Aza (11.28.2004 @11:07:57 AM EST)
Roger Duthie (11.28.2004 @11:59:37 AM EST)
Jeremy McNamara (11.29.2004 @10:38:00 AM EST)
Animesh Shrivastava (11.29.2004 @12:44:16 AM EST)
R. Nandakumar (11.29.2004 @09:22:41 AM EST)
Boris Silantev (11.29.2004 @11:58:24 AM EST)
Thomas Russo (11.29.2004 @12:29:21 PM EST)
Don Rice (11.29.2004 @06:03:00 PM EST)
Nitin Gupta (11.30.2004 @12:55:26 AM EST)
Alex McKale (11.30.2004 @02:03:12 AM EST)
Gangadhar NPK (11.30.2004 @06:44:05 AM EST)
Bert Fischer (11.30.2004 @07:39:17 AM EST)
Rethnakaran Pulikkoonattu (11.30.2004 @07:54:51 AM EST)
Aditya Utturwar (11.30.2004 @10:41:50 AM EST)
Emile Joubert (11.30.2004 @01:29:11 PM EST)
Mike Sebastian (11.30.2004 @03:59:10 PM EST)
Aaron Prenot (11.30.2004 @03:59:33 PM EST)
Reejis Stephen (11.30.2004 @09:44:00 PM EST)
Bill Webb (11.30.2004 @11:13:24 PM EST)
Vishal Mamania (12.01.2004 @06:59:41 AM EST)

Part 2
Colin Bell (11.01.2004 @01:19:07 PM EST)
Joseph DeVincentis (11.01.2004 @01:44:26 PM EST)
Raicho Tchalkov (11.01.2004 @03:33:54 PM EST)
Eugene Vasilchenko (11.02.2004 @10:30:05 AM EST)
Ari (11.02.2004 @02:56:08 PM EST)
Siva Dirisala (11.02.2004 @09:58:27 PM EST)
Vincent Vermaut (11.03.2004 @06:57:37 AM EST)
Dan Dima (11.03.2004 @08:08:32 AM EST)
Vineet Dwivedi (11.03.2004 @11:48:28 AM EST)
Jose H. Nieto (11.03.2004 @05:44:13 PM EST)
Kim Se Kwon (11.03.2004 @11:52:26 PM EST)
Daniel H. Li (11.04.2004 @03:09:12 AM EST)
Frank Mullin (11.04.2004 @04:56:54 PM EST)
Divyesh Dixit (11.04.2004 @06:07:12 PM EST)
Dharmadeep Muppalla (11.05.2004 @01:42:33 AM EST)
Troy Lee (11.05.2004 @02:39:14 PM EST)
Radu Grigore (11.05.2004 @03:03:30 PM EST)
Nirmal Balaraman (11.05.2004 @05:52:34 PM EST)
Bhimasankar Raju Potturi (11.06.2004 @10:45:52 PM EST)
Patrick J. LoPresti (11.07.2004 @08:10:07 PM EST)
Allan Lazarovici (11.08.2004 @06:44:52 PM EST)
Patrick Coleman (11.09.2004 @03:29:00 AM EST)
David Friedman (11.11.2004 @06:41:07 PM EST)
Jeff Shute (11.12.2004 @01:35:31 AM EST)
Michael Brand (11.12.2004 @02:23:01 AM EST)
Praveen Kumar J (11.13.2004 @04:02:02 PM EST)
Alexandru Sofronia (11.14.2004 @12:50:51 PM EST)
Kennedy (11.15.2004 @01:46:47 AM EST)
Chauncey Zheng (11.15.2004 @10:22:42 PM EST)
Thomas Rast (11.16.2004 @04:58:08 PM EST)
Claudio Baiocchi (11.17.2004 @10:30:13 AM EST)
Chu-Wee Lim (11.17.2004 @04:29:20 PM EST)
Max Alekseyev (11.18.2004 @07:26:23 AM EST)
Forrest McClellan (11.18.2004 @04:12:27 PM EST)
Alex Tikhonov (11.21.2004 @01:33:36 AM EST)
Daniel Chong Jyh Tar (11.21.2004 @04:08:26 AM EST)
Muharrem Gorkem (11.22.2004 @03:47:56 AM EST)
Franco Bassi (11.22.2004 @05:15:08 PM EST)
Alan O'Donnell (11.23.2004 @09:51:00 AM EST)
Dion K Harmon (11.24.2004 @02:57:32 AM EST)
Ananda Raidu (11.24.2004 @07:12:37 AM EST)
George Chen (11.24.2004 @11:46:27 AM EST)
Mark Pilloff (11.25.2004 @08:52:27 AM EST)
Jinhong Kim (11.25.2004 @09:38:40 AM EST)
Fakrudeen Ali Ahmed (11.26.2004 @01:46:40 AM EST)
John G. Fletcher (11.26.2004 @11:04:18 AM EST)
Rubén Hernández Aza (11.28.2004 @11:07:57 AM EST)
Roger Duthie (11.28.2004 @11:59:37 AM EST)
R. Nandakumar (11.29.2004 @09:22:41 AM EST)
Boris Silantev (11.29.2004 @11:58:24 AM EST)
Thomas Russo (11.29.2004 @12:29:21 PM EST)
Bert Fischer (11.30.2004 @07:39:17 AM EST)
Harsha (11.30.2004 @07:16:43 AM EST)
Emile Joubert (11.30.2004 @01:29:11 PM EST)

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