Badge Credit Card Sized Phase Calculator バッジ

Another way to determine the phase color using Chinese Remainder Theorem instead of modulo 6. Can be done faster mentally then memorizing division tables, or repeated subtraction. This works on the principle of breaking modulo 6 into modulo 3 and modulo 2. Modulo 3 is unqiue in that you can apply the Chinese remainder theorem, where you can Sum up the digits in the number until a remainder is reached that is a single digit. If the digit is divisible by 3 (so if the single digit is 3,6, or 9), then the remainder is 0; mod 3 = 0. Then apply modulo 2, which is if the original number is even, then the color of the phase is stays at zero, blue. As seen in the colors in chasing arrow diagram. If the original number is odd, then the phase color is be next in the cycle, red. If the sum of the digits ends up to be 1, 4 or 7, then the remainder is 1. If the original number is even (say the original number is 10 so 1+0=1, and 10 is even, then the phase color stays at the remainder red 1. If the original number is odd (say 91, so 9+1=10, then 1+0=1, and 91 is odd, then the phase color is the next cycle, black). If the sum of the digits ends up to be 2, 5, 8, then the remainder will be 2. Again if the original number is even, then the phase color stays at black. If the original number is odd, then the phase color cycles to blue.