BET ONE · 2026-10-21

BET ONE: A Better First Question

Compare yes-or-no questions on four possible answers. A balanced split reduces the largest group that could remain after a reply.

Hide one number from 1, 2, 7 and 8. The solver may ask yes-or-no questions and wants to keep the worst-case number of remaining candidates small.

“Is it greater than one?” separates one card from three. A yes answer still leaves 2, 7 and 8.

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Compare the size of the two branches

“Is it odd?” separates 1 and 7 from 2 and 8. Either answer leaves two candidates.

For the stated worst-case goal, the second question makes the better first split. The comparison concerns this candidate list and this objective.

After an odd answer, ask whether the number is greater than four. That distinguishes seven from one.

After an even answer, the same threshold distinguishes eight from two. Two well-chosen answers identify the hidden number.

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Check every final branch

Draw a little question tree with answers on its branches. Every leaf should identify exactly one of the four original cards.

A repeated question adds no information if nothing has changed. Asking “odd?” again cannot separate the two odd candidates.

Change the candidates and reconsider the first question. A question useful for one list need not split another list evenly.

The BET ONE deduction game rewards questions chosen for what their answers eliminate. A clever-sounding question is useful only when it changes the remaining possibilities.

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