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silverscorpion
silverscorpion • Oct 9, 2008

Another very easy one...

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

You and 2 other people have numbers written on your foreheads.
  • 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.
Can you guess the number on your forehead? Justify your answer.
durga ch
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
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
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
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
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.

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