Question 1188291: In how many ways can 25 be expressed as the sum of three prime numbers?
A) 1 B) 3 C) 4 D) 5 E) 6
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
It is ENTIRELY " trial and error " task.
Notice that you did not specify if the used prime numbers should be all different or repeating is allowed,
so the problem has one (excessive) degree of freedom . . .
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Do some work on this yourself to find the answer.
There is only one even prime number, 2.
The sum of any two odd prime numbers is even.
The desired sum of three prime numbers is 25, which is odd.
Therefore, the sum of 25 must be using three odd primes.
Note that, the way the problem is written, it is allowable for two of the three odd prime numbers to be the same.
So......
(1) If the smallest of the three odd prime numbers is 3, then the sum of the other two must be 22.
(2) If the smallest of the three odd prime numbers is 5, then the sum of the other two must be 20.
(3) If the smallest of the three odd prime numbers is 7, then the sum of the other two must be 18.
Clearly the smallest of the three odd prime numbers can't be 11 or more.
So look for solutions in each of the three cases. Only simple addition is required.
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