Brain Teasers
Food Fight Fiasco #2
The food fight is breaking out, and you are a prisoner. To determine if you really are the brain you claim you are, the other boss asks you the following with a 30-second time limit:
He writes down the following numbers:
1, 2, 3, 4, 5, 6, 7, 9, 2, 4, 3, 9, 1, 5.
The following numbers are used to create 7 distinct 2-digit prime numbers. Note that 1, 2, 3, 4, 5, and 9 must be used exactly twice while 6 and 7 must be used exactly once. What is the sum of those prime numbers?
He writes down the following numbers:
1, 2, 3, 4, 5, 6, 7, 9, 2, 4, 3, 9, 1, 5.
The following numbers are used to create 7 distinct 2-digit prime numbers. Note that 1, 2, 3, 4, 5, and 9 must be used exactly twice while 6 and 7 must be used exactly once. What is the sum of those prime numbers?
Hint
Note that any 2 digit number can be written as 10t+u, where t is the ten's digit, and u is the one's digit.Answer
3132, 4, and 6 cannot be in the one's place because that would make the number divisible by 2. 5 cannot also be in the ones place because that would make it divisible by 5. Thus, the sum of the primes is 10(2+4+5+6+2+4+5) + 1+3+7+9+1+3+9 = 313
It is also possible to figure out the prime numbers, although that will probably take longer than 30 seconds.
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