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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.

86 comments

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

    2. 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 🙂

  1. 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. 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. 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.

    1. 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.

  2. 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.

  3. 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.

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

  5. 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. 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!

  6. 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.

    1. 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.

  7. 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!

  8. > 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.

  9. very very bad

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

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

  10. 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

  11. 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.

  12. 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. 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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