Hardest question in the world

9514 1404 393

  3

Step-by-step explanation:

The center square must be the middle digit of two 3-digit squares. Those squares must begin with an odd number (the units digit of a 2-digit prime).

The possible 3-digit squares that have a middle digit shared with another 3-digit square are ...

  121, 324, 529, 729  and  169, 361, 961

The squares cannot end in 9, because there would be no 2-digit numbers satisfying 4 Down and 5 Across in those cases. The squares sharing middle digit 6 don't work because the only square starting with 1 is even (16), meaning there is no matching prime starting with 1.

After these eliminations, we're down to ...

So, the choices for square 1 are the leading digits of 2-digit primes such that x1 and x3 are both primes. This is the case for x=1, 4, and 7.

That is, there are exactly 3 solutions. The above list, together with ...

examine the two-step equation.

−  

7

4

+  

x

4

= 2

which property of operations allows you to add the same constant term to both sides?

multiplication property of equality

division property of equality

addition property of equality

subtraction property of equality

step-by-step explanation: