Weihnachtsmann rot

Challenge from 3. December

Billiards Table

Author: Hennie ter Morsche

Project: 4TU.AMI

Challenge:

There is a large triangular billiards table standing in the pixies' lounge. The angle at corner A is 40°, whereas the two angles at B and C each are 70°. If the ball hits one of the rails AB or AC, it is perfectly reflected so that the angle of reflection is equal to the angle of incidence. However, if the ball hits the sticky rail BC or if it hits one of the three corners A, B, C, it gets stuck and stops moving.

Conveniently, Ruprecht plays with a point-shaped ball that initially is located somewhere in the interior of the triangle and that moves only along straight lines. Ruprecht wants to make a single shot that scores as many rail contacts as possible before the ball gets stuck at some rail or point.

What is the largest possible number of such rail contacts?

Artwork: Julia Nurit Schönnagel

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Possible answers:

  1. The largest possible number of rail contacts is 4.

  2. The largest possible number of rail contacts is 5.

  3. The largest possible number of rail contacts is 6.

  4. The largest possible number of rail contacts is 7.

  5. The largest possible number of rail contacts is 8.

  6. The largest possible number of rail contacts is 12.

  7. The largest possible number of rail contacts is 16.

  8. The largest possible number of rail contacts is 24.

  9. Ruprecht may score infinitely many rail contacts.

  10. The largest possible number of rail contacts depends on the length of BC.

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