1. **Stating the problem:** We want to use the numbers 1, 3, 5, 7, 9 and 2, 4, 6, 8, 10 to find combinations that sum to 17, 32, 48, 60, and 64, all from a total sum of 141. 2. **Understanding the problem:** The total sum of all given numbers is $1+3+5+7+9+2+4+6+8+10=55$. Since 141 is larger than 55, it suggests we might be summing multiple times or combining sums in some way to reach 141 and then partitioning into the target numbers. 3. **Check total sum of target numbers:** $17 + 32 + 48 + 60 + 64 = 221$, which is greater than 141, so the problem might involve sums of subsets or multiple uses. 4. **Possible approach:** Since the problem is ambiguous, let's consider if the sum 141 is the sum of the target numbers minus some overlap or if the target numbers are sums of subsets of the given numbers. 5. **Sum of given numbers:** $1+3+5+7+9=25$ (odd numbers), $2+4+6+8+10=30$ (even numbers), total $25+30=55$. 6. **Try to express each target number as sum of given numbers:** - 17: $9 + 8 = 17$ - 32: $9 + 7 + 6 + 10 = 32$ - 48: $9 + 7 + 6 + 8 + 10 + 8 = 48$ (8 repeated) - 60: $9 + 7 + 6 + 8 + 10 + 10 + 10 = 60$ (10 repeated) - 64: $9 + 7 + 6 + 8 + 10 + 10 + 14 = 64$ (14 not in list) 7. **Since repetition and numbers outside the list appear, the problem needs clarification.** **Final note:** Without additional rules (e.g., repetition allowed, operations allowed), the problem cannot be solved exactly as stated. Please clarify the rules or constraints for combining the numbers.