(BE)²= MPB, where B, E, M and P are distinct integers. Then M =
a. 2
b. 3
c. 9
d. None of these
A digit number when squared produces a 3 digit number. This means that the number ranges from [10, 31].
First digit of BE² should be unit digit of E^2.
But unit digit of E is B.
Look at the numbers and the unit digit of their square.
0-0, 1-1, 2-4, 3-9, 4-6, 5-5, 6-6, 7-9, 8-4, 9-1.
Only 2-4, 3-9, 4-6, 7-9, 8-4 and 9-1 are kind of pairs we are looking after.
But all the pairs except 9-1 produce a number greater than 31.
Now, the number we can form from 9-1 is 19 whose square is 361 which satisfies all the condition we are looking for.
This is the only such numberWrite Here