Solved cryptogram
Each number in Pascal's triangle is the sum of the two above it, and the rows count choices.
Mathematics Facts, sourced to Wolfram MathWorld.
Solve it yourself
This fact is a cryptogram here: 72 letters over 20 different ones, graded medium.
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What it means
Row five reads one, five, ten, ten, five, one, and those are exactly the numbers of ways to pick none, one, two, three, four or five items from five. The addition rule works because choosing three from five either includes the last item or does not. The same triangle gives the coefficients when you multiply out a binomial, and its rows sum to successive powers of two, which is the count of all possible subsets.
The claim comes from Wolfram MathWorld.
- SourceWolfram MathWorld
- CollectionMathematics Facts
- Difficultymedium
- Length72 letters, 20 of them different
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