Take a random 2-digit number that is more than 10(e.g, 96). Now, subtract the difference between the two digits of the numbers from your original number. Continue until both digits are the same(e.g,9-6=3, 96-3=93, 9-3=6, 93-6=87, 8-7=1, 87-1=86, 8-6=2, 86-2=84, 8-4=4, 84-4=80, 8-0=8, 80-8=72, 7-2=5, 72-5=67, 7-6=1, 67-1=66 please note that I took the longest one). Name that number x(e.g, x=66). Now, take the sum of the 2 digits and call it y(e.g, 6+6=12 so y=12). Take the product of the both digits(means first digit * second digit) and name it z(e.g, 6 * 6 = 36, so z is 36). Now, take
(x-y)/z(e.g, (66 * 12)/36=22)
Your answer should be 22. If not, please tell me in the comments and I will see if you had a calculation error or something.
Now time for me to explain why this works.
You see, in the first instruction, I covered over about you having the two same digits in your number before continuing. As you know, if there are two of the same digits in a two digit number, it is divisible by 11. So, we will call this number 11x. The last digit stands for 1x while the first digit stands for 10x. Next, let us take the sum of the two numbers. Simple. Just 2x. Lastly, let us take the product of the two digits. Also quite simple. Just x(x). Now, let us take:
(x-y)/z
Easy. Just take (11x(2x))/x(x). Looks tough right? Don't worry, I have simplified it for you. Now, it is:
(22(x)(x))/x(x). Then it cancels out to 22. That's it. 22.
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