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The best is the 9's table, how all the digits add up to 9. My mom's an elementary teacher and there's always a few third graders who figure that out on their ow
by PascLeRasc 8y ago
The best is the 9's table, how all the digits add up to 9. My mom's an elementary teacher and there's always a few third graders who figure that out on their own and love it.
- sdenton4 8y agoI was legit angry that I didn't learn about the divisibility checks for 3 and 11 until college...
- somethingroma 8y agoAdditionally 9 * n = [n-1, 10-n] for n = 2-11; where n-1 is the digit in the 10's place and 10-n in the single place. This just an aesthetic curiosity. I know the pattern continues for larger n I've just never bothered to generalize it. Also never compared it to other bases.
- Koshkin 8y ago> [n-1, 10-n] for n = 2-11 I think the usual 10 * n - n makes more sense and is much easier to remember.
- sdenton4 8y agoIt's not an aesthetic curiosity at all! 10 is equal to 1 mod 9... So suppose X is written in base 10 (a0 * 10^0 + a1 * 10^1 + a2 * 10^3 +...) and you want to find X mod 9. Then all of the 10^k's are just 1 (mod 9), so you just get the sum of the digits. So if X is divisible by 9, then the sum of the digits (mod 9) is zero. Same works for 3 (x is div by 3 iff the sum of the digits id divisible by 3). And 11 gets an /alternating/ sum of the digits, since 10 is -1 mod 11...