![]() ![]() Going one set of digits at a time, changing all the other numbers to zero, we could boil down each set as +/- n* (where x>=y and n is the digit) = +/-n *10 y * (10 x-y - 1) = 10 y * (a number composed of only nines) = a number divisible by 9. Why? For every digit in the original number it appears somewhere else in the other number. The answer is always going to have a sum of digits divisible by 9. Then subtract the smaller number from the larger number. Then rearrange the digits to make a second number. Now that we have that proof out of the way we can look at this magic trick. + d n, or the sum of digits, is divisible by 9, then the entire number must be divisible by 9. 9*any integer is evenly divisible by 9. ![]() ![]() + d n*10 n, where d n is the first digit, d n-1 is the second, and so on. 36 divides evenly by 9, so 702739222 must also be divisible by 9. Let’s try it on the phone number of the Las Vegas Tropicana (70). If the sum of digits of a number is divisible by 9 then the number it self is divisible by 9. Often these mind reading number puzzles work because an interesting mathematical oddity. ![]()
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