How many perfect squares use the digits at most once?
As an explicit example, 4 and 49 satisfy the conditions of the problem.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
Square numbers only end with 4 or 9 according to the instructions given as we are only allowed to use 2 , 4 , 6 , 9
This will help us speed up the search for these "special numbers"
An example
We want to know the last two digits of 2 7 1 2
So, we rearrange the number like this:
5 0 × 5 + 2 1
It is said that the last two digits of 2 7 1 2 is equal to the last two digits of 2 1 2
Checking, we see that it is!
2 7 1 2 = 7 3 4 4 1 , and 2 1 2 = 4 4 1
We can use this to prove that there are no more solutions to this question, as we know that most square numbers do not end with the numbers 2 , 4 , 6 , 9 , thereby excluding most of the "presumed solutions"
After checking all the square numbers, you must be forced to accept that...