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## #1 Re: Puzzles and Games » Sum of 3 digits and its compliment to 1000 » 2012-12-17 22:08:18

Wow first time using this forum so I didn't expect an answer as thorough as scientia's.  I wish I had more bonus points to give out.

Julianthemath that is the correct way to start, there are three patterns to be found depending on the initial three digit value you subtract.

## #2 Re: Puzzles and Games » Prove √5 is irrational... » 2012-12-17 09:42:37

Thanks a lot, that is great help.

Apologies about the confusion with posting in two forums.

Jack

## #3 Re: Help Me ! » Prove √5 is irrational... » 2012-12-17 06:11:38

The way I tackled this so far was to say √5 = a/b

so 5 = (a/b) (a/b)  or 5x (a²/b² )

5b²  = a²

So let a = 5x
a²  = 25x
25x = 5b²
5x = b²

I have no idea if this is the right approach but it made sense when I initially wrote it,  seems a bit iffy looking back as I dont really know where I was going with this.  I think I was going to look for even numbers of prime factors but cant recall why.

## #4 Help Me ! » Prove √5 is irrational... » 2012-12-17 05:46:56

jackme12
Replies: 4

I posted this in puzzles but think it belongs here...  my bad.

Can anyone give advice on how to go about proving route 5 is irrational?

## #5 Puzzles and Games » Prove √5 is irrational... » 2012-12-17 05:43:43

jackme12
Replies: 10

As the subject says, can anybody prove that route 5 is irrational?

## #6 Puzzles and Games » Sum of 3 digits and its compliment to 1000 » 2012-12-17 05:42:40

jackme12
Replies: 7

Can you notice any patterns in the sums of the digits in three digits numbers and the sums of the digits of their complements to 1000.

For example 1000 - 255 = 745

2+5+5 = 12
7+4+5 = 16
12+16 = 28

Bonus points for multiple patterns,
Bonus bonus points for anyone who can find a direct proof.