Please do NOT post your answer, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

Imagine that there are 2 trees in a garden.  Let us call them Tree A and Tree B.  Now imagine that there some birds on both trees.

The birds on Tree A say to the birds on Tree B: ‘If one of you comes to our tree, then our population will be the double of yours.’

Then birds on Tree B say to the birds on Tree A: ‘If one of you comes to our tree, then our population will be equal to that of yours.’

How many birds are there in each tree?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle(UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

1. kroketje says:

30 seconds to work it out.

1. -M- says:

No spoilers yet? Wow…

2. Dave says:

3. Dave's Neighbour says:

One of the birds has just hatched some eggs. This has suddenly invalidated my original answer

4. Chuck Collis says:

Needed to sketch it out and took a minute or two.

5. Evieban says:

forgot how to do simultaneous equations but knew that both populations had to be small enougn if one either way could make the difference between double and equal populations…took a couple of minutes 🙂

2. Anonymous says:

Done – about a minute, but had to resort to pen and paper for the simultaneous equations as its too early in the morning to solve them otherwise 🙂

1. Lazy T says:

Early mornings get me differently, I reached for the pen and paper then did it in my head before I’d written x or y

2. ivan says:

Simul Eqns is too heavy for what has to have a solution in fairly small numbers. 10 seconds by trial and error, in my head. And I’m more than usually tired this Friday.

3. Anne Elk says:

4. Anders says:

more or less a minute.

5. What a pretty little simultaneous equations puzzle. Less than a minute.

6. Niva says:

Simple algebra will solve this one (what I did). Trial and error will also work. About 45 secs.

7. About a minute using simultaneous equations.

8. Not got a solution, yet, but I have proved that 6 = 4.

1. -M- says:

That’s even more impressive!

2. Gus Snarp says:

I used the algebra approach and arrived at a similar problem, so I had to go back and figure out if it was supposed to be impossible, or if I had set out my equations wrong. Turned out to be the latter. So it took me a few minutes.

9. I solved it with my computer. The answer is “some”.

10. -M- says:

Took me 7 lines of algebra.

1. -M- says:

(with the last 2 lines being A = … and B = …)

11. Anonymous says:

it’s a little bird puzzle – no need to throw loads of maths at it! Took me about 5 minutes in my head. I am proud of that, so thanks for stretching my brain a little.

12. Just under one minute with pen and paper and good old simultaneous equations

13. How can I admit this?- it took me an hour !

14. I wrote it down properly and did the solution for simultaneous equations formally, and took about 2 minutes. If i had thought in pictures or by instinct, I probably would have been quicker.

15. Anonymous says:

It’s a fairly simple problem, but I decided to use matrices for it (if only for a bit of practice).

16. Matt says:

Took me about 7 seconds to figure it out in my head.
If I’d had a pen and paper it probably would have taken me 5 seconds.

1. mittfh says:

I see what you did there… 🙂

2. Anonymous says:

Lol….

17. Solved it immediately. That one was too easy!

1. Dave says:

18. Anonymous says:

Solved using equations on post-it in about 30 seconds. Probably could have done by trial and error just as quick.

19. I’ve just bought “Are you smart enough to work at Google?” so I’ll be otherwise engaged puzzle-wise for the next couple of weeks.

1. Dave says:

Thanks for letting us know.

2. Try some of those puzzles, Dave. They’re pretty good.

20. Alistair says:

If you assume that the second statement is premised on the first statement actually happening, then there is another correct answer. However, I don’t think you can really read it like that!

1. Anonymous says:

That’s something I’m wondering. I worked it out quite quickly as a bird going from A to B or a bird going from B to A. Haven’t put any thought into the second statement following an action from the first.
Something to look forward to at lunctime…. as well as lunch, of course!

21. ctj says:

it took me about … wait, the birds can talk?!

1. Anonymous says:

Yes but they’re not for sale. They’re too expensive – not going cheap!

2. Anders says:

the question didn’t posit it was the feathered kind. Some birds talk a lot

22. Basically, there are no birds in either tree. I don’t know what they are but if they can do that level of maths then they sure ain’t birds.

23. mittfh says:

Ooh, the wonders of simultaneous equations 🙂 Resolve the relationship between A and B, work out the value of B, then use that to help determine A. Plug the values back into the original equations and verify they work.

24. Anonymous says:

After a bad minute, it took a second minute to solve.

25. Birds can’t speak, at least not of math,and I thought you were too close minded to believe in the paranormal Richard! 😉

1. ivan says:

Several species of parrots, and some other birds, can be trained to talk. African Grey Parrots are the best, and some make sufficiently appropriate comments they appear to understand what they are saying. Some have also been trained to do simple arithmetic.

26. Jim Cole says:

Too easy for an old math teacher…

27. I think this may be an example of one of Richard’s puzzles that can’t be solved. It doesn’t make sense to me, unless he’s describing something to do with quantum physics. It says that I have to imagine that there some birds on both trees. I’m not clever enough to do that. Some birds on each tree I can picture, but birds on both trees? It’s beyond me!

1. Lazy T says:

Nice one,that’s very picky, but if you imagine VERY big birds…..

28. Took four or five minutes. But over half of that was getting the original simultaneous equations wrong

29. dcoi says:

10 seconds. Including time to read puzzle

30. 37 in Tree A, 192 in Tree B

The birds in Tree A were lying. The ones in Tree B are bad at math.

31. Russ Ingram says:

About 3 min. No algebra . . . Moving pennys back and forth.

32. tombsar says:

> imagine that there some birds

For a blog feature that so often relies on subtle interpretations of language, I am disappointed that Mr. Wiseman does not seem to proof-read his posts at all.

33. I solved by guess-and-check. I liked the puzzle because I was surprised by which way my first guess was off.

34. issa hamati says:

about 5 sec ,but it is nice

35. Wendy Hawkins says:

No idea how to do simultaneous equations, but can use a pen and paper very well. Took about 30 secs. 🙂

36. Anonymous says:

Grade 8 Math – easy peasy!

37. Anonymous says:

the problem is not well posed

there are 2 solutions depending if the populations where the birds arrive should satisfy the property with the other population before or after the bird moving

1. Anonymous says:

My observation also. Simultaneous equations are applicable if you switch the word ‘yours’ with ‘your current population’ in the problem statement.

2. Anonymous says:

oops. (Need to read my own posts before posting). Actually simultaneous equations are applicable in either case.

38. They started hurling themselves at some cross looking pigs and exploding before I could count them….

1. LOL! Just had to let you know that I got a kick out of this. 🙂

39. Chris says:

I always forget to look at the clock, so i can only make an educated gues combined with my subjective sense of time that i spent 20-40 of my thoughts for trial and error to get a fitting solution. Now its time for bed, the birds in the trees outside are already long time quiet!
And i was very happy that Dave`s Neighbour didn’t show up today to whisper anything like a solution!!

Good nite
Chris

40. Merari says:

And people say you will never use algebra again. Poppycock.
0.5 minutes.

41. peter says:

Talking birds?

1. One Eyed Jack says:

You’ve never heard a talking bird?

42. I have an answer, though I had to assume that what the birds said was true. If they’re wrong, then the answer could be anything…

43. Dharmaruci says:

was easy. we know the nos must be quite low as no bird has ever been found in labority conditions to be able to count into double digits.

then there are some constraints. if the pops are the same if one bird migrates (Condition B) we know the initial diff between the pops. and we know from the doubling rule whether pop B +1 is even or odds. so we know if pop B was even or odds to start with.

with all those clues it takes only a few trials and errors to arrive at an ans.

1. One Eyed Jack says:

Certainly you’ve heard of Counting Crows? 😉

44. One Eyed Jack says:

I am officially predicting a discussion on Monday…

When Richards says, “If one of you comes to our tree, then our population will be the double of yours”, it can be interpreted two ways. Let the pedantic discussions begin.

1. Anders says:

Let me start it now, does the population really increase before all immigration papers are signed? Do birds need a visa? Are we talking about permanent resident birds or just vagrants? Have both trees signed the Schengen treaty?

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47. Anonymous says:

One sec easy I am good at math

48. Anonymous says: