The amazing Amber. Amber has been amazing her friends with a math trick. Amber h

Question

The amazing Amber. Amber has been amazing her friends with a math trick. Amber has a friend select a three-digit number and reverse the digits. The friend then finds the difference of the two numbers and reads the first two digits of the difference (from left to right). Amber can always tell the last digit of the difference. Explain how Amber does this.
Hint:
Let's say Amber's friend picks the number abc that is: a*100 + b*10 + c.
Reversing the digits will be cba that is c*100 + b * 10 +a
The difference of the two numbers is xyz that is x*100 + y*10+z
Start with finding the difference of the two numbers abc-cba based on the above assumptions and set that equal xyz . That is:
xyz = abc-cba

Explanation / Answer

Let the three digits be x,y and z. Now the number initially was 100x+10y+z Aftre reversing the number becomes 100z+10y+x. The difference of these numbers is 99x-99z=99(x-y). Now once the two digits are known as because the number is divisible by 3 and 11 and we know that a number is divisible by 3 if the sum of the digits be divisible by 3 ,and for 11 the a sum of 1 st plus third must be equal. So its quite easy to find the number.Check out for youself with any example. Say x=1,y=2 z=3 , so number is 123 after reversal its 321 . so difference is now 321-123=198 .Now you see if i know 19 as because for divisibility of 11 we must have the las digit 9(ie 8+1=9). So its quite easy

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