Question 25 of 25advanced🔍 AnalyzeNumerical3 marks

I'm made of digits, each tiniest and odd, No shared ground with root #1—how odd! My digits count, their sum, my root— All point to one bold number's pursuit— The largest odd single-digit I proudly claim. What's my number? What's my name?

Correct Answer

Step 1: 'Each tiniest and odd' — all digits are odd (1, 3, 5, 7, 9)

Step 2: 'No shared ground with root #1' — digital root is not 1

Step 3: 'The largest odd single-digit' — digital root is 9

Step 4: For digital root 9, digit sum must be multiple of 9

Step 5: Smallest number with all odd digits and digit sum 9: 135

Verification: Digits: 1, 3, 5 (all odd) Number of digits: 3 (odd) Sum of digits: 1 + 3 + 5 = 9 (odd) Digital root: 9 (largest odd single-digit)

Answer: The number is 135.

Exercise: Digital Roots | Q: 1 | (Page Page 19)
For More Understanding

Explanation

The chapter discusses digital roots. Analyzing the riddle: 'Each tiniest and odd' means all digits are odd (1, 3, 5, 7, or 9). 'No shared ground with root #1' means the digital root is not 1. 'My digits count' (number of digits), 'their sum' (digit sum), 'my root' (digital root) — all point to the same number. 'The largest odd single-digit' is 9. So the digital root is 9. For a number with all odd digits to have digital root 9, the sum of digits must be a multiple of 9. The smallest such number with all odd digits is 135 (1+3+5=9, digital root=9).

Solution Steps

  1. Step 1: 'Each tiniest and odd' — all digits are odd (1, 3, 5, 7, 9)

  2. Step 2: 'No shared ground with root #1' — digital root is not 1

  3. Step 3: 'The largest odd single-digit' — digital root is 9

  4. Step 4: For digital root 9, digit sum must be multiple of 9

  5. Step 5: Smallest number with all odd digits and digit sum 9: 135

  6. Step 6: Verify: 3 digits (odd), sum = 9 (odd), digital root = 9

Previous