Subject: Re: Matter of Age
Date: Mon, 10 Aug 1998 08:36:57 -0400
From: Alex Bogomolny
The lucky number can't be arbitrary. It is 90 for a good reason. The age numbers are requested to be two digit. These two conditions insure that the number at stage c has three digit and starts with 1.
Removing 1 on the left and adding it to the remaining number is the same as subtracting 99 from the original number, right?
If you wish 80 to be your lucky number, you have to insure that the number at stage c is bigger than 100. So that you can remove 1 from the left. Let your friend's age be 34:
34 + 80 = 114,
1 + 14 = 15,
15 + 19 = 34,
19 being the difference between 99 and your lucky 80.
In your case, and if you insist there should be no limitation on the spectator's age, let it be 18. Then 18+80 = 98. Now, you must declare that if the result has only two digits you remove the (nonexistent) 0 from the front of the number and add it to the remaining (which is the same) number 98+0=98. (You may as well skip this operation to avoid unnecessary explanations and, perhaps, embarrassment.)
This is the number you are given. Add to it 19 to get 117. Remove 1 now and add it to the remaining number: 1+17=18. It again works but becomes less interesting for spectators.