Janes number trap

JaneFairfax · 2009-10-11 09:44:13

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bobbym · 2009-10-11 10:12:16

Hi Jane;

First 2 things:

1) Are you sure that this is new? Just asking because there are a lot of these.

2) Like to see the proof.

mathsyperson · 2009-10-11 10:22:24

Bobby is right, this is related to Happy Numbers.
A number is defined as Happy if it eventually goes to 1, and Unhappy if it eventually goes to the loop.

JaneFairfax · 2009-10-11 10:25:15

I know Soroban has done one for cubes. If hes already done this for squares, then my apologies my search didnt turn up anything similar from Soroban.

Im not one hundred per cent about my proof yet if I do manage a proof, it probably wont be a rigorous one.

Last edited by JaneFairfax (2009-10-11 11:34:12)

JaneFairfax · 2009-10-11 10:26:19

mathsyperson wrote:

Bobby is right, this is related to Happy Numbers.
A number is defined as Happy if it eventually goes to 1, and Unhappy if it eventually goes to the loop.

Yup.

http://www.artofproblemsolving.com/Foru … p?t=305170

wintersolstice · 2009-10-17 02:16:36

There is a simple prove to this.

Firstly

This means that a number will always go under 4 digits and loops can only contain numbers between 1-3 digits.

So test all numbers (proof by exaustion) below a 1000 and that's the proof

Last edited by wintersolstice (2009-10-17 02:19:35)

mathsyperson · 2009-10-17 03:33:08

You'd also need to show that 81n < 10^(n-1), for n ≥ 4.
That's not a problem though.

wintersolstice · 2009-10-29 07:40:59

mathsyperson wrote:

You'd also need to show that 81n < 10^(n-1), for n ≥ 4.
That's not a problem though.

Thanks:D I knew my proof was a little incomplete, I just wasn't sure was else was needed

Math Is Fun Forum

#1 2009-10-11 09:44:13