Flying Birds

 A puzzle kept me awake most of the night and its still boggling my mind.

Backstory: I belong to many WhatsApp groups, one of which is a group for the members of my predegree class of 2001 (yeah I know what you're thinking. Dont say it out loud though). Someone posted this puzzle on the group yesterday:

Some birds were flying and met a bird in their way. The bird greeted them, hello hundred! They said we are not hundred, we need half of us plus you to make us hundred.

Question - how many birds were flying?

Possible answers are -

A. 198

B. 49

C. 66

D. 51

E. 101

F. 199

I copied the script verbatim for a reason.

My default answer was 199:

(x/2) + 1 = 100

(x/2) = 100 - 1 = 99.

x/2 = 99

x = 99*2 = 198.

Total number of birds flying = 198 + 1 bird they met = 199.

But the poster said it's wrong. I wasn't the only one who derived this answer, but the poster kept insisting that we got it wrong.

The other posted answers are 198 and 66. The person who supplied the 66 answer used the formula "x + 2x + 1 = 100" i.e.

x + (x/2) + 1 = 100.

x + (x/2) = 100 - 1 = 99.

3x/2 = 99.

3x = 99*2 = 198.

x = 198/3 = 66.

But the question remains how many birds were flying?

You'd think ChatGPT would know the answer, right? I must tell you it was just as confused as we were. I pushed the same question four times and it came up with 4 different answers!

Here is what I think: if a certain number of birds are flying (say y) and meet another single bird (say z) on their way, the total number of birds flying would be y + z. We know the value f z to be 1 (single bird).

Then to make a hundred, if 100 = (y/2) + 1 then we get y = 198. And total number of birds flying would be 199.

But if the puzzle had said "we are not YET hundred, we need half of us plus you" then we know that the formula would be 100 = y + (y/2) + 1 = 3y/2 then we get y = 66. And the total number of birds flying would be 67.

But 67 is not an option in the list of possible answers

What do you think? Does anyone know the solution?