Begin by drawing a 2 by 2 grid with row and column headers for students to see. Place a 6 and 9 in the first row and an 18 in the second blank of the second row. Explain this is just like the multiplication table. The numbers to the left tell us what we are counting by and the numbers on the top tell us how many we have counted.

To solve this riddle students may notice that to achieve 9 they must be counting by 1, 3, or 9. They can eliminate 9 from the first row entry as they cannot count by 9's and reach 6. Therefore, the first row entry must be a 1 or a 3. From there, they should be able to fill in the rest of the table.

An alternative strategy is to consider what 9 and 18 have in common. We can reach both 9 and 18 by counting by 9's or by counting by 3's, so the top of this column must be a 3 or a 9. Similarly, 6 and 9 can be found by counting by 1's or by 3's.

Provide students with time to try to find the missing values and allow them to share their thoughts and strategies.