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silverscorpion • Oct 9, 2008

# Another very easy one...

HI
My turn to twist ur brains..Answer this simple question..

• You are all told that the numbers on your foreheads are prime and that they form a triangle with a prime perimeter.
• You see 5 and 7 on the other 2 people.
• All three of you claim you do not know the number on your forehead, starting from you and now again it is your turn.
durga ch • Oct 10, 2008
in a triangle sum of 2 sides is greater third side

so , if x is the unknown number
7+5>x;
x+5>7;
x+7>5;

this leads us to result 12>x>2;
the intermediate primes are 3,11, 7,5
can two people have same numbers?
if not then my forehead has either 11 or 3 wirtten on it..

so if x=3 then sum is 3+5+7=15 which is not a prime number ( discarded)
if x=11 sum = 7+5+11 =23 is a aprime number

so.. the number on my head is 11 ( if any only if all three of us have different numbers written on our forehead)
silverscorpion • Oct 11, 2008
Hi durga,
Sorry I didnt mention this, but two people can have the same number on their foreheads. Now how does this change your answer??
durga ch • Oct 11, 2008
oh in that case...
assuming x=5
5+5+7=17 which is also prime
if x=7
7+7+5 is 19 which as well is prime...

so x can take any of 5 ,7 ,11
silverscorpion • Oct 11, 2008
no, x cannot take any value. There's only one value x can take..
U r on the right track, try a bit more...
electron1212 • Oct 12, 2008
Hi Guys,
I am also agree with Durga. Reason being, after considering all the constraints there are 3 possible solutions i.e. 5, 7 and 11. All three of these satisfying the condition so no way of discarding any 2 values, Untill and unless number written on foreheads are unique and if that is the case 11 is the desired number.