Two Quickies to Explore Quickly
Quickie #1: Take 4 dice. Can you place them in a square array such that the differences between the touching sides equals 2 in each case?
Quickie #2: I am thinking of three numbers, called P, Q, and R. If P is the average of Q and R, and R is twice the sum of P and Q, explain why (without using algebra or even a pencil!) one of the numbers I thought of must have been zero...and which one?
Solution Commentary: Rather than provide solutions, let me suggest an extension. In the first problem, can you do the same thing using 8 dice, this time forming a 2x2x2 cube? Or, in the original problem, could the common difference be 0?