# What are the numbers?

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Look at the calculation below. Every alphabet represents a different digit from 1 to 9 to make the calculation.

What are the numbers?

posted Sep 16, 2014

## 1 Solution

17
x 4
68
+25
93

solution Sep 17, 2014

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+1 vote

What are the largest and smallest 5-digit numbers that satisfy the following conditions?

A. Each digit of the number is a prime digit.
B. Each successive pair of digits forms a 2-digit number that is NOT a prime number.
C. Each of the prime digits must appear at least once in the 5-digit number.

Two whole numbers, m and n, have been chosen. Both are greater than 1 and the sum of them is less than 100. The product, m × n, is given to mathematician X. The sum, m + n, is given to mathematician Y. Then both mathematicians have the following conversation:

``````X: "I have no idea what your sum is, Y."
Y: "That's no news to me, X. I already knew you didn't know that."
X: "Aha! Now I know what your sum must be, Y!"
Y: "And now I also know what your product is, X!"
``````

Let us say there are two natural numbers "L" and "R".
We performed eight operations on these two numbers as

Step-1: L = R
Step-2: L x L = R x L
Step-3: L^2 - R^2 = LR - R^2
Step-4: (L + R)( L - R) = R(L - R)
Step-5: L + R = R
Step-6: R + R = R
Step-7: 2R = R
Step- 8: 2 = 1

What is wrong here?