Math Puzzle: Day of the WeekDate: 02/04/98 at 10:18:24 From: Griffin, William Subject: Why does the following math problem work Dr. Math, My question is, why does the following math problem work, irrespective of what number you use 0 - 7 for the day of the week? Here is the question; 1. First of all, pick the number of days a week that you would like to go out. 2. Multiply this number by 2. 3. Add 5. 4. Multiply it by 50. 5. If you have already had your birthday this year, add 1748. If you haven't, add 1747. 6. Last step: Subtract the four-digit year that you were born. RESULTS: You should now have a three-digit number: The first digit of this was your original number (i.e. how many times you want to go out each week). The second two digits are your age! It really works. This is the only year that this problem will work. Again thanking you in advance. William Date: 02/04/98 at 16:24:12 From: Doctor Sam Subject: Re: Why does the following math problem work This is a number trick that seems magical when you do it with numbers but is not too hard to understand if you use a little algebra. 1. Start by calling the number you pick N. 2. Your first step is to multiply by 2. This gives 2N 3. Now add 5. In algebra notation this gives 2N + 5 4. Multiply by 50. This gives 50(2N+5) which can be simplified to 100N + 250 5. Now add either 1748 or 1747. This gives: 100N + 250 + 1748 or 100N + 250 + 1747 which simplify to 100N + 1998 (had birthday) or 100N + 1997 (no birthday yet) 6. Subtract your birth year. If you have had your birthday, then if you subtract your birthyear from 1998 (this year) you will get your present age (try it!) If you haven't had your birthday yet, then 1997 was the last year you had a birthday. Subtract your birthyear from 1997 and you will again get your age. In both cases, the algebra shows that you are left with 100N + your age. So, for example, if you had started with 7 and you are 23 then you now have 723. Since you are multiplying N (your chosen number) by 100, this shifts the number to the left and adds two zeros to the number. These two zeros "make room for" your age, which will fit nicely iinto the last two spaces of your number. By the way, the algebra shows that you do not have to restrict yourself to the numbers 1 through 7. ANY whole number should work because 100N will still end up looking like a number ending in "00". Of course, it will only be a three digit number if you choose N = 1, 2, 3, 4, 5, 6, 7, 8, or 9. I hope that helps. Date: 02/04/98 at 16:40:16 From: Griffin, William Subject: RE: Why does the following math problem work Stupendous, Dr. Math. You are right, when you look at the problem algebraically it does make sense. Thank you so much. William |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/