Chance bounds
Some counts are missing. Keep every arrangement that fits the clues, then judge the claim.
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One extra clue · Narrow the possible arrangements before judging a claim.
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6 questions · No time limit
Example
Example
Example · Standard
What does the information tell you about this claim?
| Tiles | Count |
|---|---|
| All tiles | 36 |
| With marking A | 18 |
| With marking B | 18 |
A and B may overlap. The four separate groups have not been counted.
Extra clue: the number of tiles with neither marking is at most 4.
Draw one tile uniformly from all 36 tiles.
Claim: the chance of having both markings is at most 7/36.
- Questions answered
- 0 / 6
- Active time
- 0:00
Ready to start?
Read the counts and the claim. Decide whether the claim is guaranteed, possible but not guaranteed, or impossible.
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Reload pageOptional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is usedHelp
A and B are two markings. Each tile can have both, one or neither. A draw selects each tile with the same chance. The missing overlap is not assumed to be random: consider every arrangement consistent with the clues. The review shows the possible range and complete arrangements that support or disprove the claim. These are original reasoning questions, not a validated intelligence assessment.
Each round has six questions and no time limit. Choosing an answer locks it. Review the steps, then move to the next question. Finish all six to save the round. Active time includes reviewing the steps, but does not count time when this page is hidden. Speed does not affect your score.
Use Tab and Enter or Space to choose an answer. The number keys also select answers, except when another control is focused. After an answer, Enter goes to the next question.
Original practice puzzles, not a standardized assessment.
About this practice
Learn a method
Bound the missing overlapSome counts are missing. Keep every arrangement that fits the clues, then judge the claim.
Report a problem
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is used