Number Playground
One number, many ways to write it. The number stays the same. Only the way it is written changes. Made for the series Numbers at Four Ages, inspired by a draft chapter by 陈诗峰 Shifeng Chen.
1 · Match them up (ages 5+)
Add apples and stones. If every apple gets exactly one stone and nothing is left over, the two piles have the same number, even though apples are not stones.
2 · Write one number every way (ages 9+)
The last column counts symbols. That count is how long the number is to write: the thing number systems were invented to shrink.
| Way of writing | What it looks like | Symbols | Length |
|---|
3 · The carrying machine (ages 11+)
Press +1 and watch a digit fill up. In base N, a place holds 0 to N−1. One more and it rolls over to 0 and carries 1 to the left: “when you reach N, carry one.” Zero-free mode uses the digits 1 to N instead, so it never writes 0.
4 · Is it about the number, or how it is written? (ages 11+)
Tap N if the sentence is about the number itself. Tap R if it is about the representation, the way the number is written. The test: write every number in base 3 instead of base 10. If the sentence is still true, it is about the number.
Two sentences are on the border on purpose. Argue about them with someone. Arguing is the point.