Unit 2 · Number Theory

Reverse the Digits — Which Comes First?

Lesson 7 of 18

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About this lesson

Digit-reversal puzzles always become algebra: call the tens digit a and units b, then turn “reversed number is 72 more” into 9b − 9a = 72.

Chapters

0:00Introduction
0:20The Question
1:04Uncovering the Secret Pattern (The "Rule of 9")
1:40Finding the Difference Between Lena's Digits
2:11Isolating the Correct Starting Number
2:45Exam Strategy — Eliminating Extremes Instantly
3:21Confirming the Final Option

Question

Sam writes down the number 35. He reverses the digits to make the number 53. He then works out that 53 is 18 more than his starting number, 35.

Lena 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 first digit of Lena's starting number?

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