Number on Forehead Riddle

Since,

(i) 30 – 20 = 10
(ii) 30 + 20 = 50

You either have 10 or 50 on your forehead.

However if case (i) happens & you have 10 on your forehead, the person with number 30 on his forehead can see numbers 10 & 20 following which he knows that he must either have

(iii) 20 – 10 = 10, or
(iv) 20 + 10 = 30

On his forehead. However, since he cannot have 10 on his forehead (to maintain uniqueness as that number is already taken), he would “know” that the number on his forehead must be “30”.

But we are told that this did “not” happen (as apart from me, the other two persons too could not determine their numbers initially itself).

Hence, this contradiction proves that case (i) cannot happen.

Thus, the only possibility is case (ii) & this satisfies the problem from the perspective of the other two persons too as follows (in case (ii), I have number “50” on my forehead):

For person with number “20”, he thinks that he either has (undecided):
(v) 50 + 30 = 80, or
(vi) 50 – 30 = 20

While for the person with number “30”, he is “undecided” initially between:
(vii) 50 + 20 = 70, or
(viii) 50 – 20 = 30

Thus the number on my forehead is 50 (Answer).