A Square and New Dice
Two simpler problems this week:
In a 3x3 grid, place the numbers 1 to 8 in the outside squares such that
on each side of the grid, the two corners sum to the number between them.
One of my daughter's new games is called "Sum Swamp". It comes with two
regular dice and a third (6-sided) "operation" die.
The operation die has three
"+" symbols and three "-" symbols. To determine the distance to move, all
three dice are rolled. If a "+" appears, the numbers on the regular dice
are added. If a "-" appears, the smaller (or equal) number is subtracted
from the larger (or equal) number. What are the probabilities of each possible
roll, and what is the average roll for these dice?
Source: Gabe, citing Hard to solve brain teasers. Original.
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