If she adds two pennies, she can only arrange the pennies in a straight line.
A straight line is one penny wide. If she adds two pennies she ends up with a prime number of pennies.
Since she has between 40 and 50 pennies, she can have 41, 42, 43, 44, 45, 46, 47 ,48, or 49 pennies.
41 + 2 = 43 prime
42 + 2 = 44 not prime
43 + 2 = 45 not prime
44 + 2 = 46 not prime
45 + 2 = 47 prime
46 + 2 = 48 not prime
47 + 2 = 49 not prime
48 + 2 = 50 not prime
49 + 2 = 51 not prime
Only 43 and 47 are prime.
That means she has 41 or 45 pennies.
41 is prime, so it cannot be arranged in any other way than a straight line 1 by 41.
Let's look at 45.
45 = 3 * 3 * 5
45 = 9 * 5 = 3 * 15 = 45 * 1
She has 45 pennies.
