Test your skills of deduction with the May 2022 edition of Riddle Me This: Numbered Forehead
You are in a room with two perfectly intelligent men, Eugene and Frank, and a painter, Claude. Claude has painted a unique number on each of your foreheads. Each number is a whole number greater than zero, and one of the numbers is the sum of the other two. You, Eugene, and Frank all know this information.
You see the number “20” painted on Eugene’s head and the number “30” painted on Frank’s forehead.
Claude then asks you, “Do you know what your number is, and if so, what is it?” You reply “no” because at this point it is impossible for you to deduce which number you have painted on your forehead.
Claude then asks Eugene the same question, to which Eugene also replies, “no.”
Claude then asks Frank the same question, to which he also replies, “no.”
Claude then turns to you and asks once more, “Do you know what your number is, and if so, what is it?”
How do you respond this time?
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Seems like the answers have to be yes and 50. This is because 50 is the only number that is the sum of 20 and 30 such that only one of the group has the sum of the other two numbers.
“You are in a room with two perfectly intelligent men, Eugene and Frank, and a painter, Claude.”
That sentence alone is gold.
You have to be either 50 or 10. When Frank answers he sees a 20 and your number you know he is thinking he is either 30,10 or 70 and Eugene is seeing a 30 and your number and is thinking he is either 40,20 or 80. Since they know that they are unique numbers by process of elimination and since you know they are 30 and 20 respectively you have to be 10.
Two choices: 10 and 50….Must be 50. Cant be 10.
The answer is 10