IBM Research | Ponder This | May 2002 challenges

# Ponder This

## May 2002

Ponder This Challenge:

Definitions:
In the plane, call a point a "lattice point" if both its coordinates are integers, so that (2,-3) is a lattice point but (1,3.5) is not. A "circle" is the curve, not the 2-dimensional figure enclosed in that curve; it is described by giving its radius and the coordinates of its center.

Problem:
Part 1:
Describe a circle in the plane which passes through exactly seven lattice points.

Part 2:
Find such a circle with minimum radius.

Part 3:
Find (up to symmetries) all such circles with radius less than 50.

Unfortunately we won't be able to respond to answers to parts 2 and 3 this time.

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: 05/01/2002 @ 9:00 AM EST
Solution: 05/31/2002 @ 3:00 PM EST
List Updated: 06/10/2002 @10:00AM EST

Part 1 Correct
Graeme McRae (5.3.2002 @ 10:00 AM EDT)
Vitaly Stakhovsky (5.3.2002 @ 10:00 AM EDT)
Chuck Carroll (5.3.2002 @ 10:00 AM EDT)
Arjun Viswanathan (5.3.2002 @ 10:00 AM EDT)
Truman Ng (5.3.2002 @ 10:00 AM EDT)
Stephen Oman (5.3.2002 @ 10:00 AM EDT)
Claudio Baiocchi (5.3.2002 @ 10:00 AM EDT)
Keith Peters (5.3.2002 @ 10:00 AM EDT)
Jim Boyce (5.3.2002 @ 10:00 AM EDT)
Kennedy (5.3.2002 @ 10:00 AM EDT)
David H. Jones (5.3.2002 @ 10:00 AM EDT)
Vladimir Sedach (5.3.2002 @ 10:00 AM EDT)
Christof Schmalenbach (5.3.2002 @ 12:00 PM EDT)
Vince Lynch (5.6.2002 @ 10:00 AM EDT)
Philippe Fondanaiche (5.6.2002 @ 10:00 AM EDT)
Paul P. Gardner (5.6.2002 @ 10:00 AM EDT)
Hassan Masum (5.6.2002 @ 10:00 AM EDT)
Lou Cairoli (5.6.2002 @ 10:00 AM EDT)
Dave Wood (5.6.2002 @ 10:00 AM EDT)
Jacques Willekens (5.6.2002 @ 10:00 AM EDT)
Nancy Schwarzkopf (5.6.2002 @ 10:00 AM EDT)
Ignacio Larrosa Canestro (5.6.2002 @ 10:00 AM EDT)
Samantha Levin (5.7.2002 @ 10:00 AM EDT)
Al Zimmermann (5.7.2002 @ 10:00 AM EDT)
Dipankar Das (5.7.2002 @ 10:00 AM EDT)
Manish Kumar Singh (5.7.2002 @ 10:00 AM EDT)
Roy Murphy (5.7.2002 @ 10:00 AM EDT)
Srinath Anantharaju (5.7.2002 @ 10:00 AM EDT)
Mike Meehan (5.7.2002 @ 10:00 AM EDT)
Alan O' Donnell (5.7.2002 @ 10:00 AM EDT)
Chandrashekar Shankar (5.8.2002 @ 11:00 AM EDT)
Bill Schwennicke (5.8.2002 @ 11:00 AM EDT)
Christopher Howe (5.9.2002 @ 2:00 PM EDT)
Francis Golding (5.9.2002 @ 2:00 PM EDT)
John G. Fletcher (5.9.2002 @ 2:00 PM EDT)
Hajo Luers (5.13.2002 @ 10:00AM EDT)
Mitchell Kaplan (5.13.2002 @ 10:00AM EDT)
Gaurav Saxena (5.13.2002 @ 10:00AM EDT)
Mihai Cioc (5.21.2002 @ 12:00PM EDT)
Dave Biggar (5.21.2002 @ 12:00PM EDT)
Manikandan. B.J. (5.28.2002 @ 11:00AM EDT)
Fred Henle (5.29.2002 @ 11:45AM EDT)
Joaquim carrapa (5.29.2002 @ 11:45AM EDT)
Thomas Russo (5.30.2002 @ 4:00PM EDT)
Ricardas Svarplis (5.30.2002 @ 4:00PM EDT)
John vanRyneveld (6.03.2002 @ 3:00PM EDT)

Part 2 Correct
Hajo Luers (5.14.2002 @ 5:00PM EDT)
Mihai Cioc (5.21.2002 @ 12:00PM EDT)
Fred Henle (5.29.2002 @ 11:45AM EDT)
Joaquim carrapa (5.29.2002 @ 11:45AM EDT)
Ricardas Svarplis (5.30.2002 @ 4:00PM EDT)
Al Zimmermann (6.10.2002 @ 10:00 AM EDT)

Part 3 Correct
Hajo Luers (5.14.2002 @ 5:00PM EDT)
Mihai Cioc (5.21.2002 @ 12:00PM EDT)
Fred Henle (5.29.2002 @ 11:45AM EDT)
Ricardas Svarplis (5.30.2002 @ 4:00PM EDT)

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