Piny the Elder was often asked what his favorite number was. He would often settle the disputes by saying this:
PINY
+ THE
ELDER
"My favorite number is PINY in the above equation."
(Every letter is consistent throughout, and no number is represented by more than one letter.)
One day when he said this, a listener said, "My favorite number is 1537, a number such that its first two digits add up to an even number, and also such that each of the two middle numbers is between the first and last numbers. How many of these two conditions does your number meet?"
Upon hearing the answer to this, the follower knew what Piny the Elder's favorite number was. What was it?
I find the following possible solutions to the problem:
9842 + 671 = 10513
9642 + 871 = 10513
9872 + 641 = 10513
9672 + 841 = 10513
9735 + 481 = 10216
9435 + 781 = 10216
9845 + 371 = 10216
9345 + 871 = 10216
9875 + 341 = 10216
9375 + 841 = 10216
9785 + 431 = 10216
9485 + 731 = 10216
of these...
none seems to have a unique number of conditions true.
Unless I am mistaken in my analysis, it is unfortunate that the problem indicates that the answer is unique.
Edited on April 24, 2004, 10:03 am
solution
