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Education

Anyone know anything about Happy Numbers?

17 replies

GraceUnderFire · 28/10/2006 12:15

No, they're not a new band.

Ds1 is (just now...grrr) starting his maths homework. He has been given some example numbers and he has to establish whether they are 'happy' or 'unhappy'.

This is what I've found online -

A happy number is a number for which the sum of the squares of the digits eventually equals 1. For instance, 203 is happy:

203 : 2squared + 0squared + 3squared = 13
13 : 1squared + 3squared = 10
10 : 1squared + 0squared = 1

Well, we get that - he's done two so far: 23 and 17. 23 is happy; 17 is not (17 just goes on and on and on - pages of working out).

He has to choose 10 other numbers himself and work out if they are happy or not.

The last question on the worksheet is "can you tell if a number is happy without working it out?"

That's where I'm stuck - can you? He's been doing prime numbers so I thought that might be it - but 17 and 23 are both prime yet one is happy and one is not.

Help would be greatly appreciated.

As would patience (me saying through gritted teeth "you've had seven days to do this...")

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GraceUnderFire · 28/10/2006 12:46

Happy Numbers - mmm, that's a misnomer if ever I heard one.

We got 17 wrong - don't know now if it's happy or not: we're on page 3 of workings out.

I just shouted and banged the table. I am a Bad Mum who is not, never was, never claimed to be any good at maths.

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NotQuiteCockney · 28/10/2006 12:49

17 is not.

If at any point checking a number, you end up with any of the following numbers:

4 -> 16 -> 37 -> 58 -> 89 -> 145 -> 42 -> 20 -> 4

Then you're on to a loser, and it is not a happy number.

17 -> 50 -> 25 -> 29 -> 85 -> 89 ... and there ya go, you're in the loop.

cite .

NotQuiteCockney · 28/10/2006 12:50

Here are the first happy numbers:

1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68

No, there isn't an easy way to tell.

another webpage about it

GraceUnderFire · 28/10/2006 12:53

NQC, you're a star - thank you.

Walter doesn't look happy, does he?

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NotQuiteCockney · 28/10/2006 12:54

He looks like he's just been arrested. IMO.

GraceUnderFire · 28/10/2006 12:56

It's gobbledegook though, isn't it? There is no pattern to it - so ds1 can't make good guesses at which might be happy or not. Unless I use that stuff to help him and point him in the direction of happy numbers he'll be at this for hours.

I hate maths.

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GraceUnderFire · 28/10/2006 12:57

Thank you again though - much appreciated

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NotQuiteCockney · 28/10/2006 13:10

This isn't really maths. Well, the wikipedia entry calls it "recreational maths" - it doesn't really mean anything, iyswim, it's just a "fun" game.

GraceUnderFire · 28/10/2006 13:17

Oh loads of fun. Ds1 has said he's not comfortable using the sheet I printed off from Wikipaedia - "it's kind of cheating, isn't it, Mum?" I am not happy with him spending the last two days of half term in a pointless number generating/page filling exercise.

So we're in deadlock

I've written an explanatory note on the printout for his teacher - that makes it not cheating, in my books. Without that list of unhappy numbers to refer to I think you could go on for infinity...

Did I say I hate maths?

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GraceUnderFire · 28/10/2006 13:17

Even "not really maths"

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NotQuiteCockney · 28/10/2006 13:21

You could claim to have noticed the loop on your own? It's not that hard to realise you're in a loop.

Must say, I don't quite see the point to this, it's not actually very useful as maths go. It's arithmetic really, only more pointless. How old is he?

GraceUnderFire · 28/10/2006 14:17

He's 9 (year 5). We just talked about that, actually - I suggested he say something along the lines of no, you can't tell which are un/happy without working it out but the ones which are happy only take a few 'moves' to get to 1 - the unhappy ones go on...and on...and on...so you can generally assume you're not going to get to a resolution.

No, I don't see the point either and have said as much in my (polite) note.

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NotQuiteCockney · 28/10/2006 18:11

Mr. NQC here - as addition order doesn't matter than any permutation of digits of a happy number is also happy - so if 23 is happy then 32 is as well. If 17 is unhappy then 71 is as well. So you can check plenty of them without working them out.

NotQuiteCockney · 28/10/2006 18:57

Hmm, Mr. NQC says there is another loop that doesn't end with the "happy" state.

GraceUnderFire · 28/10/2006 20:59

I'll read that again in the morning - but thanks Mr NQC.

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NotQuiteCockney · 28/10/2006 21:46

Hmmm, Mr NQC has just pointed out that the other loop is 0 -> 0 -> etc.

Let's play "guess who has a maths degree" then, shall we?

More usefully, the loop detailed on the other webpages is a short-cut to telling if a number is "unhappy" - if while working through it, you hit any of those loop numbers, that's it, you're stuck.

GraceUnderFire · 29/10/2006 08:57

I think I get that - about the permutations of digits not mattering.

I've persuaded ds1 to 'cheat' anyway - and use the number list from wikipaedia as a starting point - otherwise it's just a pointless number crunching exercise. Dh backed me up when he got home from work and told him "you know, it's not proper maths..."

Wonder what we'll have next week? Depressed and mildly euphoric numbers?

Thanks again.

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