[Guest]

Substitute each of the capital letters in bold by a different base ten digit from 0 to 9 to satisfy this alphametic equation. Each of A, P and R is nonzero.

AREA = (PI)*(R)²

[Guest]

R can not be less than 4 as it will not make a 4 digit number otherwise when mult by PI

A can not be more than 7 as 98*81 = 7938 (max values of PI and R²)

R can not be 9 either because if R² = 81, I must be same as A

Only possible values of R are 4,6,7 and 8

So, if A is odd, the only possible value for R is 7

If A is odd, no set of R and I satisfies the conditions except when A is 1, R is 7 and I is 9

then AREA must be 17E1 and R² = 49

There is no value of E for which this is integer

So, A must be even (2,4 or 6)

Sets of A R and I that satisfy the conditions are:

A R I

2 7 8

2 8 3

2 4 7

2 6 7

4 7 6

4 6 1

4 6 9

4 8 6

6 4 1

6 7 4

6 8 4

6 8 9

of these the only possible solutions are:

4704 = 49*96

and 4864 = 64*76

since in the latter there is a repetition, there is only one soln:

4704 = 96 * (7)²

[Guest]

4 7 0 4 = 9 6 * (7)^2

A R E A = P I * ®^2