There are infinitely many pairs of numbers whose sum equals their product.
However, there is only one solution to the equation below, in which each letter stands for a single, distinct digit.
AB × C.DE = AB + C.DE
What digit does each letter in this equation represent?
AB × C.DE = AB + C.DE
=> C.DE (AB-1)=AB
DE AB 1
=> C + ...... = ----------- = 1 + -------
100 AB-1 AB-1
since (AB-1)^(-1) is obviously less than 1, it follows that:
C=1 and.
100
DE = ---------
AB-1
Hence, AB-1 must divide 100
Accordingly, we have:
AB-1= 10,20,25,50 , disregarding factors having leading zeros.
=> AB= 11,21 26, 51
We observe that except for AB=26, each of the other three values has B=1
This is a contradiction since the letter C has already been assigned that value.
Therefore, AB =26
Hence, DE = (100)/(25) =04, so that: (D, E) = (0,4)
Consequently, we must have:
(A,B, C, D, E) = (2, 6, 1, 0, 4) , so that:
26 x 1.04 = 26 + 1.04
Edited on May 17, 2022, 11:16 pm
Puzzle Solution
