A bird lover is asked how many birds he has in his basket. He replies: "All are parrots but six, all are pigeons but six, and all are koels but six." Based on this information, how many birds are there in the basket in total?

Introduction / Context:
This is a well known logical puzzle involving three types of birds in a basket. The owner describes the collection using three similar statements, each mentioning that all birds are of one type except six. The key is to interpret these sentences correctly and turn them into a simple system of equations for the numbers of parrots, pigeons, and koels. Once interpreted properly, the arithmetic is straightforward.

Given Data / Assumptions:

• Let the basket contain parrots, pigeons, and koels only.
• Statement 1: all are parrots but six, so all birds except six are parrots.
• Statement 2: all are pigeons but six, so all birds except six are pigeons.
• Statement 3: all are koels but six, so all birds except six are koels.
• Let the numbers of parrots, pigeons, and koels be p, q, and r respectively.
• Total number of birds is N = p + q + r.

Concept / Approach:
The phrase “all are parrots but six” means that the birds that are not parrots number six. That is, the non parrots are the pigeons and koels, whose total is six. Similarly, “all are pigeons but six” implies that non pigeons (parrots plus koels) total six. And “all are koels but six” means non koels (parrots plus pigeons) total six. These three equations can be solved simultaneously to obtain p, q, r, and thus the total N.

Step-by-Step Solution:
Step 1: From “all are parrots but six,” non parrots are pigeons and koels: q + r = 6. Step 2: From “all are pigeons but six,” non pigeons are parrots and koels: p + r = 6. Step 3: From “all are koels but six,” non koels are parrots and pigeons: p + q = 6. Step 4: Add all three equations: (q + r) + (p + r) + (p + q) = 6 + 6 + 6 = 18. Step 5: The left side simplifies to 2(p + q + r) = 2N, so 2N = 18. Step 6: Therefore N = 18 / 2 = 9. Step 7: Hence the total number of birds in the basket is 9.

Verification / Alternative check:
We can also find individual counts: from p + q = 6 and q + r = 6, subtracting gives p - r = 0, so p = r. Similarly, from p + r = 6 and p + q = 6 you get r = q, so p = q = r. Since p + q + r = 9 and all three are equal, each type must have 3 birds. Then non parrots (pigeons plus koels) are 3 + 3 = 6, and similarly for the other two statements. This matches the puzzle description perfectly.

Why Other Options Are Wrong:
Options 8, 10, or 18 do not allow the birds to be split into three equal groups that satisfy all three conditions simultaneously. Trying to assign integer counts with those totals soon leads to inconsistencies between the equations q + r = 6, p + r = 6, and p + q = 6.

Common Pitfalls:
Many people initially misread the statements as referring to how many of each type there are, rather than to how many are not of a certain type. Another pitfall is to attempt trial and error with random numbers of birds instead of setting up simple equations. Interpreting “all are type X but six” as “the birds that are not type X total six” is the crucial insight.

Final Answer:
The total number of birds in the basket is 9.