Okay, I’ll stop right here. I don’t want to end up in H-E-double hockey sticks.

]]>That’s kind of what I recall, but I wasn’t there.

]]>Needs an ominous soundtrack

]]>Calling Kaprekar’s Constant the level zero, there are only two numbers in level one: 8,532 and 7,641. But each of those numbers is identical to each of its permutations, because they will resolve the same way no matter which order they are in when you work the iteration. So 2,358 and 8,352 both resolve to the Constant, and they are functionally equal – level 1 numbers.

8,532 has 24 permutations. 7,641 only has 23 permutations, because one permutation is 6,174, which is the constant, which is level zero.

So any number that resolves to any permutation of 8532 or 7641 is a level 3 number.

Here’s the thing I’ve just worked out: not every permutation of 8532 has a level 3 number that resolves to it. So 8532 has three numbers that resolve to itself (8600, 8710 and 8820), but 8523 and 2358 have no numbers threat resolve to them.

That’s awesome, but now I have 44 more level 1 numbers to painstakingly check, which means I’m still at the brute force level of trying to answer my original question.

]]>So the next step is to find a number higher in the chain, meaning some number that resolves to 1114 in its next iteration. Then just keep working backwards.

But I’m not sure how to work backwards in a convenient way.

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