I NEED HELP STAT PLZ PLZ PLZ Betty has between $40$ and $50$ pennies that she wants to arrange in a rectangular array. She notices she can arrange the pennies in three different ways without any gaps or spaces. However, if Betty adds two more pennies to her collection, she can only arrange the pennies in one way without any gaps or spaces: a straight line. How many pennies does Betty have?
Accepted Solution
A:
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.