The two numbers are 1 and 9.
Their product is 1×9=91\times 9=91×9=9 (one-digit), while their sum is 1+9=101+9=101+9=10 (two-digit).

Why It Works

This riddle plays on basic arithmetic where small multipliers keep products tiny, but sums can stretch further with larger partners.
Sources confirm 1 and 9 as the unique positive integer pair fitting perfectly—no other combo like 2×4 (sum 6, too small) or 3×3 (sum 6) works.

It's a classic brain-teaser seen across math forums and apps, often stumping folks until they test low factors.

Other Possibilities?

  • Strictly positive integers : Only 1 and 9 qualify, as products over 9 fail the one-digit rule.
  • Including 0 : Pairs like 0 and 10 multiply to 0 but sum to 10—yet 10 isn't "one-digit" input, breaking riddle intent.
  • Negatives : -1 and 11 (−1×11=−11-1\times 11=-11−1×11=−11, not one-digit positive; sum 10)—ruled out for "whole positive numbers" in most versions.

No multi-view debates here; consensus is clear from math sites.

Quick Test Table

Numbers| Product| Sum| Fits?
---|---|---|---
1, 9| 9| 10| Yes 1
2, 4| 8| 6| No
3, 3| 9| 6| No
1, 8| 8| 9| No

TL;DR : Go with 1 and 9 —simple, elegant, and spot-on for the riddle.**

Information gathered from public forums or data available on the internet and portrayed here.