100 using Four 9s
Jump to navigation
Jump to search
Puzzle
- It is required to express $100$ by four $9$s.
Solution 1
- $100 = 99 \frac 9 9$
Solution 2
- $100 = \paren {9 + .\dot 9} \paren {9 + .\dot 9}$
where $.\dot 9$ is interpreted to mean point $9$ recurring:
- $.\dot 9 := .9999 \ldots = 1$
Sources
- 1821: John Jackson: Rational Amusement for Winter Evenings
- 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): Rational Amusements for Winter Evenings: $146$