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## #1 2005-12-20 17:46:58

Math Guy
Member
Registered: 2005-10-12
Posts: 20

### In Search of a Magic Number

RAY: This next puzzler is mathematical in nature. Imagine two numbers, such that their product is equal to their sum. I'll give you two numbers: 5 and 1 and 1/4. You add them, and you get 6 and 1/4. You multiply them, and you also get 6 and 1/4.

TOM: You do?

RAY: You do! Now, I'm going to put on one additional condition. Both numbers have to be the same. For example, let's take 3/7ths as the number. 3/7ths and 3/7ths add up to 6/7. But, unfortunately, they multiply to 9/49ths. But if it worked, then, well, that would be the kind of answer I'm looking for.

TOM: So you're looking for whole numbers as well as fractions?

RAY: Any number you can think of. Fractions, irrational numbers, you name it, we'll use it.

Is there such a number that if you multiply it by itself the product is equal to adding it to itself?

If so, what are those numbers?

Of course zeros are not allowed, because everybody knows zero plus zero is equal to zero times zero. Zero is disqualified.

*Leave what you think is the right answer here!

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## #2 2005-12-20 18:07:17

MathsIsFun
Registered: 2005-01-21
Posts: 7,630

### Re: In Search of a Magic Number

Like these?

3+3 = 6, 3×3 = 9  (no...)
.5+.5 = 1, .5×.5 = .25  (no...)

let me think ...

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #3 2005-12-20 22:15:08

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: In Search of a Magic Number

Why did the vector cross the road?
It wanted to be normal.

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## #4 2005-12-20 23:07:15

ganesh
Moderator
Registered: 2005-06-28
Posts: 21,730

### Re: In Search of a Magic Number

Well, the beauty of two 2s don't end there!
2+2 = 4
2x2 = 4
2^2 = 4
2^^2 = 4
2^^^2 = 4
....it goes on and on!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #5 2016-08-11 15:46:40

Monox D. I-Fly
Member
Registered: 2015-12-02
Posts: 669

### Re: In Search of a Magic Number

ganesh wrote:

2^^2 = 4
2^^^2 = 4

What the heck are these???

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