Can you set your robot to find other algos with fixed points? I'm guessing it's not so simple, since this one is considered popular, but it feels to me like it wouldn't be so hard to arrive at other algos with a couple properties (bounded above and have a fixed point) that do similar things.
Eff it, we'll do it live! <running my llm...>
Eureka!:
Algorithm: sort the digits descending (D) and ascending (A), then compute
f(n) = 9999 − ((D + A) mod 10000)
- Fixed point: 3333. Check: 3333 + 3333 = 6666, and 9999 − 6666 = 3333.
- Every input reaches 3333, including repdigits, which Kaprekar has to exclude.
- There are no other cycles or fixed points
- The worst case is 44 steps, starting from 1149: 1149 → 9439 → 6557 → 6777 → … → 6667 → 5666 → 7668 → 4555 → 9890 → 9120 → 0660 → 3333
I'll dub it, YODL's constant. Please send $1M my way
npub162…atdhy
2026-09-19 16:02:19 UTC
in reply to nevent1q…wslc
Author Public Key
npub162zpxufpw8pnuytaf0gfxzkqtvk9rvcwkvppa7x57y3n7qkfpg4shatdhySeen on
wss://nostr.momPublished at
2026-09-19 16:02:19 UTCEvent JSON
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"content": "Can you set your robot to find other algos with fixed points? I'm guessing it's not so simple, since this one is considered popular, but it feels to me like it wouldn't be so hard to arrive at other algos with a couple properties (bounded above and have a fixed point) that do similar things.\nEff it, we'll do it live! \u003crunning my llm...\u003e\nEureka!:\nAlgorithm: sort the digits descending (D) and ascending (A), then compute\nf(n) = 9999 − ((D + A) mod 10000)\n- Fixed point: 3333. Check: 3333 + 3333 = 6666, and 9999 − 6666 = 3333.\n- Every input reaches 3333, including repdigits, which Kaprekar has to exclude.\n- There are no other cycles or fixed points\n- The worst case is 44 steps, starting from 1149: 1149 → 9439 → 6557 → 6777 → … → 6667 → 5666 → 7668 → 4555 → 9890 → 9120 → 0660 → 3333\n\nI'll dub it, YODL's constant. Please send $1M my way",
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