Odd and even, added
You pick 6 cards. Every card shows an odd number. Can the sum be 41?
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Step 1 of 4
- Three odd numbers as dots: 3, 5 and 7.
- Each odd number leaves one spare dot.
- Three spares make one pair and one alone.
- 3 + 5 + 7 = 15. The sum is odd.
The rule
No: six odd cards make an even sum, and 41 is odd.
An even number pairs up with no dot left over. An odd number leaves one spare. Even numbers do not change whether the sum is odd or even.
Add some numbers. Count how many are odd. If that count is even, the sum is even. If that count is odd, the sum is odd.
| How many odd numbers | The sum is |
|---|---|
| 1 | Odd |
| 2 | Even |
| 3 | Odd |
| 4 | Even |
The count of odd cards is 6, which is even. So the sum is even. 41 is odd, so it cannot be the sum.