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Two Numbers
What numbers when added or multiplied together produce the same result both ways?
Answer
2 and 2 or 0 and 0Hide Answer Show Answer
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Comments
The numbers 0 and 0 also work.
Ok, I reworked this using basic algebra as follow: X + Y = XY
Y = XY - X
Y = X(Y-1)
Y/(Y-1)= X
Test it out, it works fine. Y cannot equal 0, but there is an infinite number of solutions. For example: when y=5, X=5/4 Thus the sum is 25/4 and product is also 25/4. This is graphable and logical.
Y = XY - X
Y = X(Y-1)
Y/(Y-1)= X
Test it out, it works fine. Y cannot equal 0, but there is an infinite number of solutions. For example: when y=5, X=5/4 Thus the sum is 25/4 and product is also 25/4. This is graphable and logical.
Sorry, the browser didn't take hard returns on my last comment. Let me redo the formula: XY = X + Y, so: XY - X = Y, then, X(Y-1) = Y, then, X = Y/(Y-1). The last comment was confusing with out some separation.
3 and 1.5 also work.
this is really easy, not to mention that there are plenty of other possible answers!!!
this is really easy, not to mention that there are plenty of other possible answers!!!
Pusandave, nice work on the algebra, but actually y can equal 0. It just cannot equal 1, as then the denominator will be undefined.
good one but Dina 2002 how does 3 work
3+3=6
3times3=9
3+3=6
3times3=9
Nov 02, 2003
What Dina_2002 meant marka was 3 * 1.5 = 4.5, and 3 + 1.5 = 4.5
What about 1, 2 and 3? It didn't say it had to be two numbers, it just said 'what numbers'. 1+2+3=6 1*2*3=6
How about -1 and .5?
I was also thinking 1 ,2 , 3. On the other hand the title suggests something else that probably should have been in the body of the puzzle.
I did the same thing as pusandave.. you get an infinite number of answers.. but if your asking for integars its different.
Sep 12, 2010
The author didn't specify whether the numbers should be integers or not. if fractions apply, then there would be infinite answers, as long as they satisfy 1/X + 1/Y = 1
which would give us:
2,2
3, 3/2
4, 4/3
5, 5/4
```````
which would give us:
2,2
3, 3/2
4, 4/3
5, 5/4
```````
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