Coffee Room

Discuss anything here - everything that you wish to discuss with fellow engineers.

12914 Members

Join this group to post and comment.

# 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.

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.

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)

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)

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??

Sorry I didnt mention this, but two people can have the same number on their foreheads. Now how does this change your answer??

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

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

no, x cannot take any value. There's only one value x can take..

U r on the right track, try a bit more...

U r on the right track, try a bit more...

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.

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.