On Friday I set this puzzle….
When Jane was just eight years old she developed a bit of a crush on Jim. Jim was eighteen and decided to make a promise to Jane. He carved a heart into a nearby cherry tree and placed his initials inside the heart. The heart was out of Jane’s reach by 16 centimetres. Jim promised to marry Jane when she was tall enough to carve her initials next to his. Jane’s reach increased by 8 centimetres a year, but the tree was growing by 7 centimetres each year.
How old was Jane when she could ask Jim to keep his promise?
If you have not tried to solve it, have a go now. For everyone else, the answer is after the break.
Trees grow from their top, not their bottom. Therefore the heart will remain at the same height above the ground, and so Jane will be able to add her initials when she is ten. As a result, Jim felt something of a fool, and apologised to all concerned.
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.
November 28, 2011 at 7:02 am |
good
November 28, 2011 at 7:04 am |
Love it!
November 28, 2011 at 7:13 am |
Got it!
Had a similar question before. Otherwise I would not have known.
November 28, 2011 at 7:17 am |
Trees grow from their top, not their bottom.
Even a highly oblong, ellisoidal tree in vaccum?
November 28, 2011 at 7:32 am
Trees don’t grow in a vacuum, silly!
But, growing plants in a weightless environment is in fact reasonable, possibly viable, and even possibly vital for longer autonomous flights.
November 28, 2011 at 11:03 am
But then she can reach the carved heart…
November 28, 2011 at 4:58 pm
… consider a spherical cow…
November 28, 2011 at 7:19 am |
Totally and factually incorrect answer
November 28, 2011 at 7:37 am
Details, please!
Sure, the lower part of the trunk might grow a bit, but not by much in two years.
November 28, 2011 at 12:39 pm
Are you sure about that? http://dendro.cnre.vt.edu/forsite/howdoes.htm
November 28, 2011 at 7:19 am |
Why shouldn’t Jim marry her?
It’s political correctness
November 28, 2011 at 7:21 am |
Let’s hope Jim apologised for his concern.
November 28, 2011 at 7:33 am |
Right time to get pedantic… Why didn’t the question say “…when could she reach the heart?” Instead by saying that Jane had to be able to carve her initials next to Jim’s that raises more questions; how tall were Jim’s initials and how long was Jane’s knife?
I just assumed she had a knife with a 10inch blade and she made him marry her immediately! After all – who’s going to argue with a lovesick girl with a knife?
November 28, 2011 at 8:53 am
Thanks for this reply…..
November 28, 2011 at 6:11 pm
Well, thanks for the question, actually
November 28, 2011 at 8:06 am |
Jane was internally destroyed by this betrayal, and bore her bitter anger through her teenage years, although she told nobody. When Jim married another ten years later, it was too much, and there followed a few years later the terrible massacre of an entire family among the gentle pink blossom of a cherry tree orchard. Among these trees, one stood, blackened and burned out.
All around people were asking why? She was never to tell – what worse thing could they do to her now?
November 28, 2011 at 12:27 pm
?
November 30, 2011 at 4:30 am
lol Nice.
November 28, 2011 at 9:38 am |
How old was Jane when she could ask Jim to keep his promise?
Regardless of the height of the heart or Jane, legally she could NOT ask Jim to keep his promise until she was at least 16.
see http://www.weddings.co.uk/info/legeng.htm
etc.
November 28, 2011 at 12:33 pm
She could ask him, but nothing could come of it.
November 28, 2011 at 5:03 pm
If you want to play language semantics, you could say that she could “ask” him to keep his promise immediately. What she couldn’t do is ask him to fulfill his promise.
November 28, 2011 at 10:10 am |
Surely she could immediately say “Jim, please keep your promise”, which is asking him to keep his promise.
November 28, 2011 at 10:33 am |
Beautiful puzzle! I found “The fence wire or board doesn’t rise into the air because height growth doesn’t occur out of the ground, it only occurs from the branch tips.” at http://dendro.cnre.vt.edu/forsite/howdoes.htm
November 28, 2011 at 11:01 am |
Aha…I got one of these right for a change.
Although I imagine that to carve her initials “next” to his she’d have to grow a bit more than she would in 2 years? Because she’d only just reach the heart in that time rather than the middle of the heart where his initials would be.
November 28, 2011 at 11:10 am
My point exactly! – And what does she use to carve her initials with – her fingernails? Probably not! Therefore there must be a knife! And how long is the blade???
November 28, 2011 at 11:52 am |
I got it after a false start, seduced by apparently easy maths.
November 28, 2011 at 12:30 pm
Ditto
November 28, 2011 at 12:01 pm |
Dear Jane, stay in school, study hard and forget this loser.
November 28, 2011 at 12:02 pm |
If what you say is true, can someone explain this please?
http://www.neatorama.com/2007/05/25/a-bicycle-eaten-by-a-tree/
November 28, 2011 at 12:35 pm
It’s a hoax.
November 28, 2011 at 7:42 pm
Trees do grow outward as well. But what Richard was referring to was how a tree gains height, not width.
November 28, 2011 at 7:43 pm
… Oh, except that tree has also grown upwards as well. Oops.
November 28, 2011 at 12:20 pm |
I got the age , but I wasn’t sure about how Jim would feel. Glad he apologized.
November 28, 2011 at 2:53 pm |
Well my second answer was correct. And it only took me about 6 hours to get to the second answer
November 28, 2011 at 3:25 pm |
Bah, all my fooling round with equations was in vain because you introduced the nature into the problem. Since when did the real world have anything to do with it?
Bah. Again.
November 28, 2011 at 4:03 pm |
All I want to know is why Jane didn’t simply go and get something to stand on and carve her initials a few minutes later…
November 28, 2011 at 8:15 pm |
The puzzle asked “How old was Jane when she could ask Jim to keep his promise”
Normally there is only one day every four years when it is ok for a girl to propose to a boy. Sometimes even fewer.
If you assume that this story began on 1st March 1896, then regardless of her reach, Jane couldn’t ask Jim to marry her until 29th February 1904. By which time she’d be sweet sixteen and there would be no impropriety.
November 28, 2011 at 8:18 pm |
I got it!
November 29, 2011 at 7:37 am |
Little bit worried about Jim. What is he doing fooling around with an eight year old? And criminal damage to a tree. I thing he may be a wrong ‘un.
November 29, 2011 at 10:38 am |
Yay, got it. That was my ‘creepy real world answer’, and it’s better than the ‘weird puzzle world answer’, I guess.
November 29, 2011 at 1:37 pm |
A young short tree will have branches, but often in older trees there’s no branches for the first few meters. If the tree only grows from the top, then where do the young tree’s branches disappear? In cities you might have gardeners trimming branches lower down, but aren’t wild trees often bare towards the bottom too? Do the branches fall off when they’re not useful anymore because sunlight isn’t getting that low?
November 29, 2011 at 1:52 pm
Judging by the fact that most older trees have ‘eyes’ on their trunks that appear to be scars from where branches were once attached, I’m guessing that’s exactly what happens.
November 29, 2011 at 8:40 pm |
I expected to argue about reasonable assumptions, but I found out that my answer was wrong and I like the real one. Nice!