Relative Likelihood of n Sixes on 6n Dice/Mistake
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Source Work
1992: David Wells: Curious and Interesting Puzzles:
- The Puzzles:
- Prince Rupert's Cube
- $129$ (Solution)
- Prince Rupert's Cube
Mistake
- Our short table shows the probabilities, rounded to three decimals, of obtaining the mean number or more sixes when $6 n$ dice are tossed.
$6 n$ $n$ $\map P {\text {$n$ or more sixes} }$ $6$ $1$ $0.665$ $12$ $2$ $0.619$ $18$ $3$ $0.597$ $24$ $2$ $0.584$ $30$ $5$ $0.576$ $96$ $6$ $0.542$ $600$ $100$ $0.517$ $900$ $150$ $0.514$
Correction
The $6$th line is incorrect.
For $96$ dice, you are looking to score at least $16$ sixes, not $6$, as $\dfrac {96} 6 = 16$ not $6$.
Sources
- 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): Prince Rupert's Cube: $129$