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The Last Christmas

Posted by Karl Sharman on July 15, 2010 – 3:23 pm

In the far, far north, outside Milton Keynes, there grows a lonely tree. Legend has it that when this tree is cut down, there will never be another Christmas.
Ten years ago, a woodcutter drove a marker into the trunk of the fifty-foot tree at a point half his own height.
Not knowing of the legend of the tree, he promised himself he would finally get around to felling this lonely tree when the marker was as high as he.
So far, I am sure you are with me on the veracity of this tale. Trust me that the rest of the tale is true…
This woodsman was a bit of a legend himself- he was twenty-five feet tall ten years ago. Legends are rife in the northern reaches….
Ten years ago, the woodsman grew at a rate of a foot a year. Today he grows at only eleven inches per year. Every ten years (on the dot) his rate of growth shrinks by an inch. Someday, he will stop growing altogether….
It’s twue, it’s twue!! (Additional points for spotting where that quote comes from)
The tree, on the other hand, will grow until it is cut down at a rate of one inch per year.
If legends live forever (and were true), in how many years will the last Christmas be?

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19 Responds so far- Add one»

  1. 1. Eketahuna Said:

    Ok, will go wrong somewhere I’m sure but …
    The original marker height was 150″
    The woodsman was 300″ to start and will stop growing in 111 years, when he will be 1080″ high (I’ve allowed for the first 10 years having passed already).
    At a rate of 1 ” per year it will be 160″ now, so another 920 years … assuming of course that the tree grows purely from the bottom up, pushing all previous growth upwards, and not some convoluted way across the whole height of the tree (e.g. NOT total tree height by 1 “, but marker only goes up 1/4″)

  2. 2. Chris Said:

    The giant’s inital height was 25′ = 300″ so half that is 150″. The tree’s initial height was 50 ‘ = 600″. So the marker is 1/4 of the way up the tree. Asume the growth is unfiformly distributed along the entire tree, the marker will increase in height by 1/4″ / year.

    Clearly the giant will have grown to his maximum height long before the marker catches up with him. The giant’s final height will be 300 + 10(12+11+10+…+2+1) = 1080″ (in 120 years from now). I have assumed that the giant had just started his 12″ / year growth phase when he made the mark.

    The the marker must increase in height by 1080-150 = 930″. That will take 930/(1/4) = 3720 years. But this started 10 years ago so the last Christmas will be in it 3709 years time.

  3. 3. Chris Said:

    Blazing Saddles.

  4. 4. Chris Said:

    aargh max giant height in 110 years from now.

  5. 5. Timesnap Said:

    New Question- If this inch less groing thing has been going on his whole life, then how old is he when he stuck in the marker?

  6. 6. Timesnap Said:

    Whoops, Growing not Groing.

  7. 7. Chris Said:

    errr I think I should have said 3210 years time. My brain always struggles with the number of gaps between numbers.

  8. 8. Ping Said:

    Don’t trees only grow from the top (branches) and since the marker was initially placed relatively low on the tree it would never go up and never be at the height of the woodcutter (unless he began to shrink) and therefore Christmas will last forever.

  9. 9. Scott Said:

    Never – Trees grow from the top, the marker will not move.

  10. 10. Knightmare Said:

    i’m going to say that trees grow only at the very top.
    the marker won’t move.

  11. 11. Fat Guy Said:

    Don’t trees grow from the bottom up?

  12. 12. Anonymous Said:

    Tree growth occurs at the peripheral edges of the tree in limited spots i.e. the top and branches and the outer layer expanding outwards.

    Tree growth doesn’t occur from the bottom up or evenly throughout. This allows trees to easily “grow over” obstructions placed in their path, yet these obstructions will not move. A spike driven into a tree will not change in vertical height as a tree grows.

    Hence since the marker will not rise, we will have XMAS forever.

    Cam

  13. 13. Anonymous Said:

    Below are some links to support my assertion on the manner that trees grow,


    Cam

  14. 14. Anonymous Said:

    Below are some links to support my assertion on the manner that trees grow,

    http://www.cnr.vt.edu/dendro/forsite/howdoes.htm
    http://en.wikipedia.org/wiki/Meristem

    Cam

  15. 15. Chris Said:

    Cam’s links were didn’t appear, here they are:

    http://www.cnr.vt.edu/dendro/forsite/howdoes.htm
    http://en.wikipedia.org/wiki/Meristem

    So trees only have significant lengthwise growth at the tips of the branches.

    So it seems that the marker won’t move much, if at all.
    So we’ll be getting hankies, socks and jumpers for a very, very long time yet.

  16. 16. Karl Sharman Said:

    Here’s the maths that would give you the assumed answer….
    The woodcutter grows 120″ in the first ten years, 110″ in the second ten years, and so on. This simple series adds up to 780 inches, when added to his original height of 300 inches is 1080 inches, or an even 90 feet. The woodcutter will never get any taller.
    Clearly the marker will never overtake the woodcutter while he is growing, so the problem becomes when will the tree be ninety feet tall. And that is also simple arithmetic. The marker started at 150″, so has another 930 inches to go, or 930 years. But that was ten years ago, so the last Christmas will be in 920 years.

    But as it happens, this is Trick of Mind and this isn’t a question of simple arithmetic. It’s a question of simple biology. Trees grow upward at their extremities; only the top of the tree is getting higher, not the bottom, which just gets wider.

    The Knightmare before Christmas gets in first and saves Christmas.

    Chris also spotted Blazing Saddles and the Schiklgruber (?) moment

  17. 17. Chris Said:

    Hi Karl. You have an number of posts waiting for you to approve them, as does Knightmare.

  18. 18. Karl Sharman Said:

    Thanks Chris. Done!

  19. 19. Euclid's Brother Said:

    While I aggree with the Biology that says trees grow from the top, the marker WILL rise somewhat. I group up in a small town and we had a paster where there was bob-wired fence nailed to several trees. And everyone I can remember had the bobwire streatched upward from the adjacent posts. Granted it may take a 100 years for that to be so. And also the tension of the wire may “hold it down” somewhat.

    Something nailed to the side of a tree will rise some, but eventually, the tree will engulf it and once it passes through the center of the tree, it will be held tight and no longer rise at all. The center of the tree will hold it and the edge (however little it pushes upward) will just pass arround the object, if it’s still sticking out. (If you don’t believe me, find a tall thin sapling and tie it in a tight knot somewhere in the lower trunk area and measure it’s hight every few years.)

    With all that said. The tree will probably engulf the marker (depending on it’s size) long beofre any noticable rise.

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