Brain Teasers
The Total is 14, Part II
Mr. Simkin, the new math teacher at school, was impressed by their ability to solve logic puzzles. He pulled aside three more students, and handed them each a sealed envelope with a number written inside. He told them that they each have a positive integer, and the sum of their numbers was 14.
They each opened their envelope and inspected their numbers. Snap said, "I know that Crackle and Pop each have a different number."
Crackle replies, "I already knew that all three of our numbers were different."
Pop says, "Now I know what all three of our numbers are."
Mr. Simkin turns to the class to ask if anyone else knows the numbers. Only Gretchen raises her hand, and she correctly identifies what each person is holding. How did she know?
They each opened their envelope and inspected their numbers. Snap said, "I know that Crackle and Pop each have a different number."
Crackle replies, "I already knew that all three of our numbers were different."
Pop says, "Now I know what all three of our numbers are."
Mr. Simkin turns to the class to ask if anyone else knows the numbers. Only Gretchen raises her hand, and she correctly identifies what each person is holding. How did she know?
Answer
Snap's statement implies that his number is odd. Crackle's statement implies that not only is his number odd, but it is also greater than or equal to 7. There are only six combinations that satisfy these conditions. Namely, for (Snap, Crackle, Pop) they are:(1, 7, 6)
(1, 9, 4)
(1, 11, 2)
(3, 7, 4)
(3, 9, 2)
(5, 7, 2)
Since Pop can reason perfectly, he knows these are the possible combinations. In order for him to know the other two, he must be holding a 6, since he knew the solution had to be unique. Therefore, Snap has a 1, Crackle has a 7, and Pop has a 6.
And, as usual, Gretchen solidifies her place as a top student.
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Comments
i liked the teaser
but...
but...
i found it a little confusing
how do the statements imply what you claim they do?
how do the statements imply what you claim they do?
clever
bravo !! gr8!
i didnt get the ansa but i loved it .. math is food for the brain
awesome! it took me a bit, but i finally got it! yay me!!!
Very good teaser! I didn't even have a clue as to the answer but I enjoyed it
huh! My brain hurts! And I'm usually good at teasers!
Great job!
i dont get how they say they are odd?
nevermind, i get the answer
I thought this one was much easier than the first... then I got the wrong answer!
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