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Problem of the Day #105: Hippopotamus Hexagon Hopping July 2, 2011

Posted by Alex in : potd , trackback

There exists a two-row hexagonal grid, shown below, that extends infinitely to the right, continuing the numbering pattern shown. Albert is on hexagon $1$. A hippopotamus is on hexagon $99$. Every second, the hippopotamus jumps and lands on, with equal probability, any hexagon that is either one step closer* to Albert or the same distance away from Albert (there is a chance the hippopotamus will not move at all). If the average number of seconds it will take for the hippopotamus to reach Albert is $t$, compute $1000 t$.

Hexagonal grid
*Note: the distance between two hexagons is defined as the length of the shortest sequence of adjacent hexagons that goes between them.


1. Andrew - July 2, 2011

you should mention the hippo can stay on the same hexagon

2. Q - January 12, 2012

FALSE, it is a nown fact that biological Hippopotamus (Hippopotamus amphibius) cannot jump, especially in Africa a land without the procurements of haxagonal surface. That is a mejor flaw with the problem, unless (Choeropsis liberiensis or Hexaprotodon liberiensis) are the type of hippo being used, in which case it should be clarified.
Additionally, the Choeropsis liberiensis or Hexaprotodon liberiensis type of Hippo potami are in current situations of endangermeant. If being captured and used in a way other than beneficial to their survvial, the container of the animals must be prosecuted immidiately with accord to HRM law of South Africa, and violators shall be imprisoned until paying a fine of maximum {POUNDS.PENCE} 5000,45 . Goodday.