IBM Ponder This #172 · August 2012

Let C be the set of points with integer coordinates whose distance from the origin is no more than 1111 units.

Place three unit charges in three different quadrants in C, such that the equivalent force they apply on a unit charge at the origin is no more than 3E-12. For example, the three points (-2,-2), (-2,3) and (1,4) apply a force of ~0.121 on the charge at the origin.

Update 9/05: The best solution so far is ~4.008e-15, from Andreas Stiller; Jan Fricke; Vladimir Sedach; Peter Gerritson; Don Dodson; Mark Mammel; Tom Sirgedas; Jamie Jorgensen & Jason Lee; Patnaik Yasodhar, Siegbert Steinlechner; Arthur Breitman; Armin Krauss; Joël Bleuse; Giorgio Antonelli; Bradley Sherman; Arthur Vause; Deron Stewart; Anunay Kulshrestha; David Greer; Daniel Lecina; Shouky Dan & Tamir Ganor; Ioan Marius Popdan; Mark Pervovskiy; Andrea Andenna; Shilei Zang; Vincenzo Gianferrari Pini & Lorenzo Gianferrari Pini; Dan Dima and Adam Daire.

Solution

Best opened after a real attempt

To be added.