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?
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Submitted by Gamer
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Rating: 2.7143 (7 votes)
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Solution:
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First of all, all 10 numbers are accounted for in the above equation. This means that all the numbers are used in the equation.
Also note that the only way a 4 digit number plus a 3 digit number equals a 5 digit number is if the first two digits of the 5 digit number are 10, the 4 digit number begins with 9, and the hundreds place of the two smaller numbers carry. So far we have this:
9INY
+ TH1
10D1R
L=0, E=1, P=9
Notice that N+H=1, and Y+1=R can't carry. Since the numbers 2,3,4,5,6,7,8 are left, only 3 combinations of N/H work, 8/3, 7/4, 6/5. Then, Y needs to be one less than R, and this further lessens the possibilites. Two of the remaining numbers need to equal the third plus ten. Only 3 combinations of N/H, Y, R, and I/D work. I say N/H and I/D becuase these can be switched.
9872
+ 641
10513
9785
+ 431
10216
9875
+ 341
10216
Here are the three main cases.
The only way the follower would know the number was if the number fit both condtions. This eliminates the first and third main case. (and these 4 solutions) Since the second condition is met, the number must have the first part even, so this narrows the possibilities to 9785 which is both such that the first two numbers equal 16, and the 7 and 8 are both between 9 and 5.
9785
+ 431
10216
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