### Brain Teasers

# 4139 Main Street

There is an apartment building on 4139 Main Street. There is a strange thing about floor 7 of this building ... everyone is a prime age! From the clues provided, can you decipher how old these residents are?

In Suzy's age, the digits have a sum of four. Seven years from now, Suzy's age, when you add the digits together, will be 20 less than her current age. She is under 100 years old. How old is Suzy?

Jason is younger than Suzy by at least 5 years. Four years ago Jason was prime, and in 4 years Jason will be prime again. How old is Jason?

In Suzy's age, the digits have a sum of four. Seven years from now, Suzy's age, when you add the digits together, will be 20 less than her current age. She is under 100 years old. How old is Suzy?

Jason is younger than Suzy by at least 5 years. Four years ago Jason was prime, and in 4 years Jason will be prime again. How old is Jason?

### Hint

Make a list of all the possible numbers it could be, as per the clues. Then, cross them off when they don't pertain to other clues. There is only one possible answer!### Answer

To solve for Suzy's age, we must first list all the numbers under 100 with a sum of 4:4, 13, 22, 31, 40

Of these, the only prime numbers are 13 and 31. If we try the second clue on each number, we get:

13+7=20, 2+0=2, 13-2=11

31+7=38, 3+8=11, 31-11=20

Therefore, Suzy must be 31.

To find Jason's age, we should first take Suzy's age (31) and subtract 5, leaving us with 26. This is the maximum possible age Jason could be. Again, listing out all the prime numbers under 26:

2, 3, 5, 7, 11, 13, 17, 19, 23

If we add four to each of these, only 3, 7, 13, and 19 stay prime. Taking these remaining 4 and subtracting four, the only one that remains prime is 7.

Therefore, Jason must be 7.

As an interesting side note, 4139 (the street number) is prime! If you don't believe me, check for yourself!

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