An algebra problem by Yellow Tomato

Algebra Level 3

How many 2 digit numbers when flipped and added together result in a perfect square?

details and assumptions

The two digit numbers are in the form of AB where it is 10A+B, not A × \times B.

The sum is of the numbers AB and BA.


The answer is 8.

Yellow Tomato by Yellow Tomato , 17, USA

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.

1 solution

Lion Soul
Oct 26, 2015

A B = 10 A + B AB = 10A +B .

B A = 10 B + A BA = 10B +A .

A B + B A = 11 A + 11 B = 11 ( A + B ) AB+BA= 11A+11B= 11(A+B) .

Therefore A+B must me 11 for A B + B A AB+BA to be a perfect square.

Possible combinations are (9,2), (8,3),(7,4),(6,5).

From each combination we can get two numbers like 92 and 29.

Total possible Numbers = 2x4= 8 \boxed 8 .

6 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...