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What are the numbers?

–1 vote
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Sum Sam and Product Pete are in class when their teacher gives Sam the Sum of two numbers and Pete the product of the same two numbers (these numbers are greater than or equal to 2). They must figure out the two numbers.

Sam: I don't know what the numbers are Pete.
Pete: I knew you didn't know the numbers... But neither do I.
Sam: In that case, I do know the numbers.

What are the numbers?

posted Feb 25, 2016 by Saif Khanam

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3 Answers

0 votes

2 AND 2 ARE THE TWO NUMBERS

answer Feb 25, 2016 by Nithi Mani
0 votes

The numbers are 3 and 4.

Since Sam knows the sum of the numbers (x + y) he would only know the answer immediately if the sum was 4 (2 + 2) or 5 (3 + 2). Then when Pete (who knows x*y) knew that Sam didn't know the answer the product must have several numbers that add up to the sum (7 = 3 + 4, 7 = 5 + 2). When Pete doesn't know the answer at this point we know the product must have more than one pair of viable factors (12 = 3 * 4, 12 = 6 * 2). At this point Sam knows the numbers are 3 and 4 because they are the only numbers that meet these criteria.

answer Feb 26, 2016 by Avantika Agrawal
Wouldn't (2,4) and (3,3) for sum of 6 confuse him too?
Sorry my bad then the product guy would know the numbers right ?
0 votes

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, and so forth. A notational symbol that represents a number is called a numeral. In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers), for ordering (as with serial numbers), and for codes (as with ISBNs). In common usage, the term number may refer to a symbol, a word, or a mathematical abstraction.
Main number systems
\mathbb{N} Natural= 0, 1, 2, 3, 4, ... or 1, 2, 3, 4, ...
\mathbb{Z} Integer =..., −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, ...
\mathbb{Q} Rational =a/b
where a and b are integers and b is not 0
\mathbb{R} Real=The limit of a convergent sequence of rational numbers
\mathbb{C} Complex=a + bi where a and b are real numbers and i is the square root of −1
enter image description here

answer Feb 26, 2016 by Gunjan Saraswat



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