Find a three-digit number containing three different digits

[Greg Bernhardt]

Find a three-digit number containing three different digits where the following are all perfect squares:

(A) The sum of the first digit and the number formed by the second and third digits;
(B) The first digit multiplied by the number formed by the second and third digits and
(C) The sum of the three digits.

 

[Rogue]

In the midst of figuring this out I found out that I need to know if you consider zero a perfect square - some people do.

Assuming that you do my answer is

036

0 + 3 + 6 = 9
0 + 36 = 36
0 x 36 = 0


also "081"

If not, I am still finishing up all the possible ones without zeros...

 

[Rogue]

916

 

[Rogue]

A little bit about the math method I used, being a freakin' genius!

First off - assess which requirement narrows the answers down. It's the last one.

Any such X Y Z numbers must be at least one, and at greatest nine.

So at least 1 + 1 + 1
and at greatest 9 + 9 + 9

3 to 27

There are only 4 PS in that range:

4 - 9 - 16 - 25

So the only possible XYZ number is numbers that add up to those.

4 can easily be done with only a few variables. Nine takes a bit more...


4 and nine both have no such answers needed.

So on to 16, which has just the one I mentioned.

How many does 25 have? I didn't bother once I finally got one - but maybe greg knows!

My guess is less than 4!

 

[Rogue]

Hey Greg - I am new here and like this brain teaser thing.

I was wondering - I could provide some very difficult questions, ones that no one could find the answer to online, and would truly require some brain "teasing". Just PM me or something if you'd like to view any of them, thanks!