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Posers and Puzzles

Posers and Puzzles

  1. 20 Jul '06 13:50
    There is this type of leaf that grows on the surface of a pond. It happens that the leaf multiplies every 24 hours. Therefore 1 becomes 2 the next day; then becomes 4 after the second day; becoming 8 the day after and so on and so forth.

    Now it has been determined that it takes 40 days to cover up the whole surface of the pond if we start day 1 with one leaf only. OK, fine, now we take away all those leaves and start over again, this time with 2 leaves on day 1. How long does it take to cover the entire surface of the pond?
  2. 20 Jul '06 15:15
    Originally posted by ckoh1965
    There is this type of leaf that grows on the surface of a pond. It happens that the leaf multiplies every 24 hours. Therefore 1 becomes 2 the next day; then becomes 4 after the second day; becoming 8 the day after and so on and so forth.

    Now it has been determined that it takes 40 days to cover up the whole surface of the pond if we start day 1 with one ...[text shortened]... this time with 2 leaves on day 1. How long does it take to cover the entire surface of the pond?
    Still 40 days?
  3. 20 Jul '06 15:17
    No.
  4. 20 Jul '06 15:32
    39 methinks.
  5. 20 Jul '06 15:50
    20 days
  6. 20 Jul '06 15:54
    Originally posted by crazyblue
    Still 40 days?
    I would of thought 40 as well. That is if we are dealing in discrete numbers of days. Because starting with two leaves we get to the same amount as 40 days with 1 leaf starting, but minus the one that started out. So it would take that extra day just to fill the pond. But as 40 is wrong I'm going for the obvious 39.
  7. 20 Jul '06 15:54
    How do you keep an idiot in suspense?
  8. Subscriber FreakyKBH
    Acquired Taste...
    20 Jul '06 19:17 / 5 edits
    Originally posted by ckoh1965
    There is this type of leaf that grows on the surface of a pond. It happens that the leaf multiplies every 24 hours. Therefore 1 becomes 2 the next day; then becomes 4 after the second day; becoming 8 the day after and so on and so forth.

    Now it has been determined that it takes 40 days to cover up the whole surface of the pond if we start day 1 with one ...[text shortened]... this time with 2 leaves on day 1. How long does it take to cover the entire surface of the pond?
    DayLeavesLeaves
    112
    2 2 4
    3 4 8
    4 8 16
    5 16 32
    6 32 64
    7 64 128
    8 128 256
    9 256 512
    10 512 1,024
    11 1,024 2,048
    12 2,048 4,096
    13 4,096 8,192
    14 8,192 16,384
    15 16,384 32,768
    16 32,768 65,536
    17 65,536 131,072
    18 131,072 262,144
    19 262,144 524,288
    20 524,288 1,048,576
    21 1,048,576 2,097,152
    22 2,097,152 4,194,304
    23 4,194,304 8,388,608
    24 8,388,608 16,777,216
    25 16,777,216 33,554,432
    26 33,554,432 67,108,864
    27 67,108,864 134,217,728
    28 134,217,728 268,435,456
    29 268,435,456 536,870,912
    30 536,870,912 1,073,741,824
    31 1,073,741,824 2,147,483,648
    32 2,147,483,648 4,294,967,296
    33 4,294,967,296 8,589,934,592
    34 8,589,934,592 17,179,869,184
    35 17,179,869,184 34,359,738,368
    36 34,359,738,368 68,719,476,736
    37 68,719,476,736 137,438,953,472
    38 137,438,953,472 274,877,906,944
    39 274,877,906,944 549,755,813,888
    40549,755,813,888 1,099,511,627,776

    I'll go out on a limb and say, oh, 39 days.
    EDIT: Tried to get the columns to match. No luck!
  9. 21 Jul '06 00:07
    All this trouble over the least significant bit of mathematics.
  10. 21 Jul '06 00:32
    Wow... you clever people! Yes, the correct answer is 39 days, although I have a much simpler explanation that the one offerred by Freaky.

    The most significant point is that the leaves double in number each day. This means that when we started with one leaf, because it took 40 days to cover the whole surface, then it must mean that on the day prior to that, it was only half covered. It follows that on the 40th day, that half doubled up to cover the entire surface.

    OK, fine, now we imagine starting with 2 leaves. One of them will cover half of the surface in 39 days; and the other leaf does the same for the other half of the pond. Therefore, those 2 leaves cover the entire pond surface in 39 days!
  11. 21 Jul '06 08:38
    Okey, after 40 days we have 549,755,813,888 leaves covering the surface of the pond. Thats half a trillion leaves. !!!

    Consider the every leaf weigh about 10 grammes. This make 5 trillion gramms or 50 billion kilograms or 50 million tonnes of leaves. !!!

    Say we have a pond of 10 by 10 metres, 100 square metres and every leave have a surface of say 10 square centimetres. then you need 1000 leaves on every square metre. With half a trillion leaves you have to stack them half a billion leaves on top of eachother. !!!

    Say every leaf has a thickness of 1 millimetre, then the height of this stack of leaves reaches half a million metres, or 500 kilometres in height. That's outside the atmosphere up to low orbit satellites. !!!

    I don't think this scenario is plausible.
  12. 21 Jul '06 08:48
    Wow... your thoughts are really very, very far! I must admit that I didn't go that far myself. But the point of the problem is on the rational means on how to determine the number of days to cover the pond, given an earlier 40 days for a particular circumstance. I could have easily said it took, say, 10 days only to cover up the entire surface of the pond, and perhaps then it would be more realistic? In that sense, I guess my original question was a 'mistake'?
  13. 21 Jul '06 09:02
    Well, it is a good puzzle, and good puzzles don't have to be plausible.

    More of the kind!
  14. Standard member Bowmann
    Non-Subscriber
    21 Jul '06 21:43 / 1 edit
    What a bunch of twonks!

    Applying minimal lateral thinking, this puzzle is solved in one second.
  15. Subscriber FreakyKBH
    Acquired Taste...
    22 Jul '06 14:09
    Originally posted by Bowmann
    What a bunch of twonks!

    Applying minimal lateral thinking, this puzzle is solved in one second.
    It took my computer less than one second.