Posted - 04/30/2013 : 18:04:08 Three students are told the following.

1--Three positive integers, x, y and z, are written on three separate cards. 2--The three cards are placed face down on the table in the order of x, y and z. 3--The three numbers sum to 13. 4--The numbers on the cards are in increasing order on the table, i.e., x < y < z. 5--The three students are asked to determine the numbers on the cards. 6--Student #1 is allowed to take a look at card "x" without letting anyone else see the number on the card. 7--After some soul searching, the student states that he is unable to determine the numbers on all three cards. 8--Student #2 is asked to take a look at card "z" without letting anyone else see the number on the card. 9--Shortly, he also states that he is unable to determine the numbers on all three cards. 10--Student #3 is asked to take a look at card "y" without letting anyone else see the number on the card. 11--He also states that he is unable to determine the numbers on all three cards. 12--You, as an observer to these events, and not having seen the numbers on each card, are asked "What is the number on the middle card?"

2 L A T E S T R E P L I E S (Newest First)

TchrWill

Posted - 05/01/2013 : 12:35:59 Congratulations the hill1962. You are right on the money.

the_hill1962

Posted - 05/01/2013 : 12:04:50 The number on the middle card is 4. I arrived at this by listing out the possible combinations: 1. 1 2 10 2. 1 3 9 3. 1 4 8 4. 1 5 7 5. 2 3 8 6. 2 4 7 7. 2 5 6 8. 3 4 6 Then, eliminate #8 because if it was 3 4 6, student 1 would know the cards since that is the only possibility when he sees the 3. Now, student 2 has the following possible combinations: 1. 1 2 10 2. 1 3 9 3. 1 4 8 4. 1 5 7 5. 2 3 8 6. 2 4 7 7. 2 5 6 Eliminate #1, #2 and #7 because each of these is unique given the card he/she looks at (i.e. an 8 or a 7 are the only numbers that have more than one possibility). Now, student 3 has the following possible combinations: 3. 1 4 8 4. 1 5 7 5. 2 3 8 6. 2 4 7 Eliminate #4 and #5 since those are unique (i.e. he/she would know it if the middle card is a 5 and also if the middle card is a 3. So, the only two possibilities left are 3. 1 4 8 6. 2 4 7 Each having the middle card be "4"