Math Is Fun Forum

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!

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

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 ...

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

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: In Search of a Magic Number

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

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,402

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!

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: In Search of a Magic Number

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

What the heck are these???

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Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.