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Snake and Ladders



On every ends of the hollow logs  lies the nests of the  snake that lays  gold shelled eggs.
To harvest the treasures you should make a ladders  out of the logs you remove.
The snake can lay the  golden eggs on any of the available nests.
It should be able to use all the nests that you could access.
You can not cross the logs while the fierce snake won't cross the ladders .
Which logs  should be replaced by ladders for greatest income?
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Let the twenty-seven intersections be labelled as follows:

A( 1,-1,-1), B( 1, 0,-1), C( 1, 1,-1),
D( 0,-1,-1), E( 0, 0,-1), F( 0, 1,-1),
G(-1,-1,-1), H(-1, 0,-1), I(-1, 1,-1),
J( 1,-1, 0), K( 1, 0, 0), L( 1, 1, 0),
M( 0,-1, 0), *( 0, 0, 0), N( 0, 1, 0),
O(-1,-1, 0), P(-1, 0, 0), Q(-1, 1, 0),
R( 1,-1, 1), S( 1, 0, 1), T( 1, 1, 1),
U( 0,-1, 1), V( 0, 0, 1), W( 0, 1, 1),
X(-1,-1, 1), Y(-1, 0, 1), Z(-1, 1, 1)

One solution that allows each nest to be reachable by the snake via a hollow log and each nest to be reachable by 'you' via a ladder is with the following ladder placement:
AB, AJ, CL, DE, EF, E*, GO, IQ, JK, KL, KS, K*, MU, M*, NW, OP, OX, PH, PQ, P*, RS, ST, UV, VY, V*, YZ

Hollow logs remain at the following locations:
AD, BE, BK, CF, DG, DM, EH, FI, FN, GH, HI, JM, JR, LT, MO, NQ, N*, PY, QZ, RU, SV, TW, UX, VW, WZ, XY

As can be observed, each of the twenty-seven intersections are in both the set of ladders and in the set of hollow logs. (Not all ladders are needed, but were added for ease of use).
Edited by DejMar
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