Neow’s Counterexample

At a glance

• Part 1: One counterexample is Bash, Heavy Blade, and Uppercut.
• Part 2: An “every” claim must work for every allowed hand. One allowed hand that fails makes the claim false.

1. Build a counterexample

Choose Bash, Heavy Blade, and Uppercut. Each card costs 2 Energy. Whichever card the Ironclad plays first, <mj-math>3 - 2 = 1</mj-math> Energy remains. The other two cards each cost 2 Energy, so he cannot afford either one. He cannot play a second card from this hand, so the hand is a counterexample.

Other answers are possible. Any three cards chosen from Bash, Heavy Blade, Uppercut, and Bludgeon form a counterexample because each of those cards costs at least 2 Energy. After playing any one of them, at most 1 Energy remains, and every remaining card costs at least 2.

2. Why one hand is enough

Neow used the word every, so his claim must work for every allowed three-card hand. The counterexample is an allowed hand, but the Ironclad cannot play two cards from it. That single failure makes the “every” claim false.

The pictured Strike-and-Cleave hand does not rescue the claim. It proves only that at least one hand works, not that every hand works.

Check

The selected cards are different and all come from the table. Every possible first play leaves too little Energy for a second play. The counterexample meets every rule in the prompt.