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How does this work? It requires a little bit of algebra to understand. Let's call shoe size "s" and your birth year "y." Now, let's do the trick again, using these letters instead of numbers.
Multiple s by 5: 5s
Add 50: 5s + 50
Multiply by 20: 20(5s + 50) = 100s + 1000
Add 1014: 100s + 1000 + 1014 = 100s + 2014
Subtract birth year: 100s + 2014 - y
Do you see why it works? No matter what your shoe size is, it will always be the first two digits of the answer. If your shoe is 12, then 100s = 1200. If you are European and your shoe size is 36, then 100s = 3600.
The age part should be obvious. 2014 (the current year) - y (your birth year) will give your age.
But this trick does not always work. If you were born in, say, December 1982, then this trick would incorrectly conclude that you were 32 years old. In fact, you would be only 31. The trick also does not work if you are 100 years old or older. If you were born in 1914 and wear a size 10 shoe, the trick would conclude that your shoe size is 11 and that you were 0 years old.
So, if you want to impress people with a math trick this Halloween, just be sure their birthday is sometime before November... and don't show it to any centenarians!
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