5x5 Square Grid and 5 Circes

In his book Mathematical Delights Ross Honsberger tells about a letter Professor Liong-shin Hahn received from a mathematics teacher. The latter posed to his student the following problem:

Given a 5×5 square grid.

a 5x5 square grid

Find five circles so that they pass through each of the 25 grid points at least once.

One of the students reported the following solution:

a 5x5 square grid puzzle, solution 1

explaining that a straight line is nothing but a circle with an infinite radius. When the teacher insisted that the task was to find circles with finite radii, the student surprised the teacher with another diagram:

a 5x5 square grid puzzle, solution 2

To teacher's objections the student rolled the diagram into a cylinder, making all circles of finite radius:

a 5x5 square grid puzzle, solution 2 on a cylinder

Naturally, that was not what the teacher had in mind. But what was it?

The applet below illustrates the problem. It may be helpful in finding the solution.

9 January 2013, Created with GeoGebra

(An HTML5 variant of this page appears on a separate page.)

References

  1. R. Honsberger, Mathematical Delights, MAA, 2004, 155-158

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Solution

a 5x5 square grid puzzle, final solution

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