x to the x to the x, forever, equals 2. Find x without a calculator.

A positive x stacked as an infinite power tower equals 2. The story asks for x. You type your answer and check it. Then you step through the answer and the breakdown.

Why quant interviews test this

Interviewers want the self-reference step fast, then a word about convergence. The written solution is at /brain-teasers/infinite-power-tower/solution.

The The Infinite Power Tower guide covers how scoring works, the strategy that wins, a worked example and the mistakes most players make.

More Brain Teasers games

• Screwy Pirates - Five rational pirates vote on how to split 100 gold coins, and you work out the split by backward induction from a one-pirate crew up.
• Tiger and Sheep - A hundred rational tigers and one sheep on a magic island, where any tiger that eats becomes a sheep itself - solved by induction on parity.
• The Split Deal - The prisoner's dilemma played as a story: two thieves, separate rooms, and one offer each.
• Stag or Hare - The stag hunt as a story: two equilibria, and a choice that comes down to trust.
• One Offer, No Discussion - The ultimatum game as a story: one split of 100 pounds, one accept-or-reject, no negotiation.
• The Growing Pot - The centipede game as a story: a pot that doubles on every pass, and logic that says take it immediately.
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