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Timothy writes down the number 24. He reverses the digits to make the number 42. He then works out that 42 is 18 more than his starting number, 24.  Nicole writes down a whole number between 10 and 99. She also reverses the digits of her number. She finds that this makes a number that is 72 more than her starting number.  What was the last digit of Nicole's starting number? 
Overseas Competition->Knowledge Point->Number Theory Modules
Let the original number be ab, and reverse it to be ba, calculated by the place value principle, ba-ab=72  10 + a - b (10) a + b = a = 9 b - 9, 72-8 a = b, b = 9, a = 1, the original number is 19, last digit is 9. 