Question 33 of 43advanced🔍 AnalyzeShort Answer3 marks

Write a 9-digit number where exchanging any two digits results in a bigger number. How many such numbers exist?

Correct Answer

Condition: A 9-digit number where exchanging any two digits results in a bigger number must have digits in strictly ascending order from left to right.

Example: 123456789

Why it works: If we exchange any two digits, the larger digit moves to a more significant position, making the number bigger.

Note: Numbers like 123456788 or 123456779 don't work because exchanging equal digits doesn't change the number.

Answer: Only one such number exists: 123456789.

Exercise: Figure it Out (Section 6) | Q: 3 | (Page Page 20)
For More Understanding

Explanation

For exchanging any two digits to result in a bigger number, the original number must have digits in strictly ascending order (each digit smaller than the one to its right). The only 9-digit number using digits 0-9 exactly once with this property is 123456789.

Solution Steps

  1. Identify that digits must be in strictly ascending order from left to right.

  2. Example: 123456789

  3. Verify that exchanging any two digits makes the number bigger.

  4. Note that numbers with repeated digits don't work.

  5. Conclude: only one such number exists: 123456789.

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