MathLabs

Problem 4

A magician has one hundred cards numbered 11 to 100100. He puts them into three boxes, red, white and blue, each nonempty. A member selects two boxes, chooses one card from each, and announces their sum. Given this sum, the magician identifies the box from which no card was chosen. How many assignments of the cards to the three boxes make this always possible?
Step 4 of 5: Classify equality
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A,B,C are common-difference progressions or two are singletons.A,B,C\text{ are common-difference progressions or two are singletons}.
Detailed analysis

The equality characterization gives these two cases.