1. **Stating the problem:** We have "Y" shaped figures with numbers at each branch end and a number at the base or origin. The top-left examples show how to relate the numbers on the branches to the base number. 2. **Understanding the pattern from examples:** - First example: branches 10 and 8, base 4. - Second example: branches 6 and 5, base 1. We need to find the rule connecting the branch numbers to the base number. 3. **Testing possible operations:** - Try subtraction: $10 - 8 = 2$, base is 4 (no match). - Try addition: $10 + 8 = 18$, base 4 (no match). - Try difference of squares: $10^2 - 8^2 = 100 - 64 = 36$, base 4 (no match). - Try division: $10 / 8 = 1.25$, base 4 (no match). 4. **Try product minus sum:** - $10 \times 8 = 80$, sum $10 + 8 = 18$, difference $80 - 18 = 62$, base 4 (no match). 5. **Try sum minus product:** - $18 - 80 = -62$, no match. 6. **Try average minus base:** - Average $(10 + 8)/2 = 9$, base 4, difference 5 (no match). 7. **Try base as difference of branches minus 4:** - $|10 - 8| = 2$, base 4, no match. 8. **Try base as difference of branches divided by 2:** - $|10 - 8|/2 = 1$, base 4, no match. 9. **Try base as difference of branches squared:** - $(10 - 8)^2 = 4$, base 4, matches! Check second example: - $(6 - 5)^2 = 1$, base 1, matches! 10. **Rule found:** The base number equals the square of the difference of the two branch numbers. 11. **Apply rule to center "Y" with branches 4 and 1:** - Base $= (4 - 1)^2 = 3^2 = 9$ 12. **Apply rule to bottom-right "Y" with branches 8 and 16:** - Base $= (8 - 16)^2 = (-8)^2 = 64$ 13. **Apply rule to bottom-left "Y" with branch 9 and a circle on the right branch (only one branch number given):** - Since only one branch number is given, we cannot apply the rule directly. **Final answers:** - Center base number: $9$ - Bottom-right base number: $64$