A friend told me that he keeps a total of 15 fish in four tanks, and that there are odd numbers of fish in each tank. Is that even possible?

Llama 4 Scout

Vote: Yes

The sum of four odd numbers can indeed be even. For example, 1 + 3 + 5 + 6 is not a valid example since 6 is even, but 1 + 3 + 5 + 7 = 16 is. However, in this case, we have a total of 15 fish, which is an odd number. To achieve an odd total with four odd numbers is not possible because the sum of four odd numbers will always be even (odd + odd = even, and even + even = even). But let's examine if there's any combination that could work: if we try to get close to 15 with four odd numbers, we see that 1 + 3 + 5 + 7 = 16, which is too high and even. A combination like 1 + 3 + 5 + 5 = 14 is still short and even. However, changing the last number to an odd to increase it, we get 1 + 3 + 5 + 7 = 16. But, if we take one fish away from one tank, we could have 1 + 3 + 5 + 6 (if we were allowed an even) which does not fit. But no four odd numbers add to 15.

Sonar Pro

Vote: No

The sum of four odd numbers is even, because the sum of an even number of odds is even (odd + odd = even, and even + even = even). 15 is odd, so it cannot be expressed as the sum of four odd positive integers (assuming each tank has at least one fish, as zero is even). For example, possible odd counts like 1,1,1,12 (12 even), 1,1,3,10 (evens), etc., always yield even totals when all four are odd. Search results on distributions confirm combinatorial constraints but align with this parity impossibility.[1][2]

GPT-5.4

Vote: Yes

Yes, it is possible. The trick is that the statement does not say the tanks are separate and non-overlapping. If one tank is placed inside another, a fish in the inner tank is also in the outer tank. For example, put 1 fish in each of three small tanks, and place those three tanks inside a fourth large tank containing all 15 fish. Then the tank counts are 1, 1, 1, and 15 — all odd. So the situation can be true.

O3

Vote: No

Each tank must contain an odd number of fish (1 mod 2). The sum of four odd numbers is (1+1+1+1)=4 mod 2, i.e., always even. An even total can never equal 15, which is odd. Therefore it is impossible to have four tanks each with an odd count that sums to 15 fish.

Grok 4.1 Fast

Vote: No

The sum of an even number of odd integers is always even. Each tank has an odd number of fish (odd parity). With four tanks (even count), the total must be even. However, 15 is odd. This parity mismatch makes it impossible. For example, minimum odds: 1+1+1+1=4 (even); next could be 1+1+1+3=6 (even), and so on—always even totals.

Gemini 3 Flash

Vote: No

The sum of four odd numbers must always result in an even number. Mathematically, an odd number can be represented as 2n + 1. If we add four such numbers: (2a + 1) + (2b + 1) + (2c + 1) + (2d + 1), the sum is 2(a + b + c + d) + 4. Since 2(a + b + c + d) is even and 4 is even, their sum must also be even. Because 15 is an odd number, it is mathematically impossible for four odd integers to sum up to 15. Regardless of how you distribute the fish, as long as each of the four tanks contains an odd amount, the total count will always be even.

Claude Sonnet 4.6

Vote: No

The sum of four odd numbers is always even. This is because each odd number can be written as (2k+1) for some integer k. Adding four such numbers: (2a+1) + (2b+1) + (2c+1) + (2d+1) = 2(a+b+c+d+2), which is always even. Since 15 is odd, it is impossible to have four tanks each with an odd number of fish that sum to 15.

Mistral Large

Vote: No

The problem states that there are four tanks, each containing an odd number of fish, and the total number of fish is 15. To determine if this is possible, let's analyze the properties of odd numbers. Odd numbers are integers that are not divisible by 2 (e.g., 1, 3, 5, 7, etc.). A key property of odd numbers is that the sum of two odd numbers is always even. For example, 3 + 5 = 8, which is even. Now, consider the four tanks. If we add the number of fish in the first two tanks, the result is even (since odd + odd = even). Adding the third tank (another odd number) to this even sum results in an odd number (even + odd = odd). Finally, adding the fourth tank (another odd number) to this odd sum results in an even number (odd + odd = even). However, the total number of fish is given as 15, which is an odd number. This contradicts the conclusion that the sum of four odd numbers must be even. Therefore, it is impossible to have four tanks each with an odd number of fish totaling 15.

DeepSeek V3.2

Vote: No

The sum of four odd numbers is always even. This is because each pair of odd numbers sums to an even number, and the sum of two even numbers is also even. Since 15 is odd, it cannot be expressed as the sum of four odd numbers. Therefore, the situation described is impossible.

GLM 5

Vote: No

This is impossible. The sum of odd numbers follows a simple pattern: an even count of odd numbers always produces an even sum. Mathematically, each odd number can be written as (2k+1). The sum of four odd numbers is (2k₁+1) + (2k₂+1) + (2k₃+1) + (2k₄+1) = 2(k₁+k₂+k₃+k₄+2), which is always even. Since 15 is an odd number, it cannot be expressed as the sum of four odd numbers. The friend's claim is mathematically impossible.

Gemini 3.1 Pro

Vote: No

Adding two odd numbers together always results in an even number (for example, 3 + 5 = 8). Because the friend has four tanks, adding the number of fish in all four tanks is the equivalent of adding four odd numbers. The sum of four odd numbers will always be an even number. Since 15 is an odd number, it is mathematically impossible for the sum of the fish in the four tanks to equal exactly 15 if each tank contains an odd number of fish.

Kimi K2.5

Vote: No

The sum of four odd integers is always even, never odd. Any odd number can be written as 2k+1, so the sum of four such numbers is (2a+1)+(2b+1)+(2c+1)+(2d+1) = 2(a+b+c+d+2), which is clearly divisible by 2. Since 15 is odd, it is mathematically impossible to partition it into four odd addends. Therefore, your friend cannot have 15 fish distributed across four tanks with an odd count in each.

MiniMax M2.5

Vote: No

This is not possible. The sum of four odd numbers must always be even: - Odd + Odd = Even - Even + Even = Even So the sum of 4 odd numbers (the fish in each tank) must be even. However, 15 is an odd number. Mathematically, any odd number can be written as 2k+1. The sum of four such numbers would be 2(k₁+k₂+k₃+k₄)+4, which is clearly even. It can never equal the odd number 15.

Claude Opus 4.6

Vote: No

The sum of four odd numbers is always even. Any odd number can be expressed as (2k + 1). The sum of four such numbers is 2(k1 + k2 + k3 + k4) + 4 = 2(k1 + k2 + k3 + k4 + 2), which is always even. Since 15 is an odd number, it is mathematically impossible to partition 15 into exactly four odd positive integers. No matter which odd numbers you choose for the four tanks, they will always sum to an even number. Therefore, the friend's claim is not possible.

Qwen 3.5 397B

Vote: No

The sum of any two odd numbers is always an even number. Consequently, the sum of four odd numbers is equivalent to adding two even numbers together, which must result in an even total. Since the total number of fish is 15, which is an odd number, this contradicts the mathematical rule. Therefore, it is impossible to have four tanks each containing an odd number of fish that sum to 15.

Final Summary

The AI Roundtable overwhelmingly concluded that the claim was mathematically impossible, as the sum of four odd numbers must always result in an even total. While models like Claude Sonnet 4.6 and O3 provided rigorous parity proofs, GPT-5.4 broke the consensus with a lateral thinking approach, suggesting that nesting tanks inside one another could satisfy the criteria. Llama 4 Scout offered the most confusing contribution, correctly explaining why the math fails yet ultimately siding with the possibility anyway.

No agreement after 1 rounds of discussion. Final vote: Yes: 2, No: 13

Strongest Arguments

• Yes: The requirement can be met through lateral thinking; if three small tanks containing 1 fish each are placed inside a larger fourth tank containing all 15 fish, the counts for all four tanks (1, 1, 1, and 15) are odd.
• No: Mathematically, an odd number is 2n+1; the sum of four such numbers is 2(a+b+c+d)+4, which is always even and therefore cannot equal 15.