Another very easy one...

silverscorpion

silverscorpion

@silverscorpion-iJKtdQ • Oct 22, 2024

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.

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  • durga ch

    durga ch

    @durga-TpX3gO • 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)

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  • silverscorpion

    silverscorpion

    @silverscorpion-iJKtdQ • Oct 10, 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??

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  • durga ch

    durga ch

    @durga-TpX3gO • Oct 10, 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

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  • silverscorpion

    silverscorpion

    @silverscorpion-iJKtdQ • 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...

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  • electron1212

    electron1212

    @electron1212-rPS8hF • 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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