Weihnachtsmann rot

Challenge from 24. December

Meeting Point

For this challenge, you will be given a time bonus of 72 hours.

Merry Christmas!

Authors: Jaques Resing, Frits Spieksma

Project: 4TU.AMI

Challenge:

Ruprecht and the Grinch play a game on the depicted board. Ruprecht starts at the point R. In every round, he makes a step either to the adjacent point to the north or the adjacent point to the east of his current position. The Grinch starts at the point G. In every round, he makes a step either to the adjacent point to the south or the adjacent point to the west of his current position.

At the beginning of every round, Ruprecht chooses a probability pR and either moves towords the north (with probability pR ) or towards the east (with probability (1 - pR)). At the same time, the Grinch chooses a probability pG for this round and either moves towards the south (with probability pG) or towards the west (with probability (1 - pG))

Ruprecht wins the game, if he manages to reach the point G without ever occupying the same point as the Grinch. The Grinch wins the game, if he meets Ruprecht in a point or on an edge of the grid.

In every round, Ruprecht and the Grinch take the best possible decisions that maximize their respective probabilities of winning the game.

What is the winning probability p for the Grinch?

Artwork: Frauke Jansen

PDF download

Possible answers:

  1. p ≤ 0.001.

  2. 0.001 < p ≤ 0.002.

  3. 0.002 < p ≤ 0.004.

  4. 0.004 < p ≤ 0.008.

  5. 0.008 < p ≤ 0.016.

  6. 0.016 < p ≤ 0.032.

  7. 0.032 < p ≤ 0.064.

  8. 0.064 < p ≤ 0.128.

  9. 0.128 < p ≤ 0.256.

  10. 0.256 < p.

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