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.

1. @davebakedpotato says:

Love it!

2. M says:

Got it!

Had a similar question before. Otherwise I would not have known.

3. Navneeth says:

Trees grow from their top, not their bottom.

Even a highly oblong, ellisoidal tree in vaccum?

1. M says:

But then she can reach the carved heart…

2. One Eyed Jack says:

… consider a spherical cow…

4. Hugh Janus: says:

1. Michael Sternberg says:

Sure, the lower part of the trunk might grow a bit, but not by much in two years.

5. Anonymous says:

Why shouldn’t Jim marry her?
It’s political correctness

6. Charles Sullivan says:

Let’s hope Jim apologised for his concern.

7. Peter O says:

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?

1. Berhard says:

2. Anonymous says:

Well, thanks for the question, actually 🙂

8. Steve Jones says:

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?

1. Camel Ali says:

?

2. Anonymous says:

lol Nice.

9. Martin says:

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.

1. A Robot says:

She could ask him, but nothing could come of it.

2. One Eyed Jack says:

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.

10. Richard says:

Surely she could immediately say “Jim, please keep your promise”, which is asking him to keep his promise.

11. Tomas Blomberg says:

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

12. Paul says:

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.

1. 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???

13. Lazy T says:

I got it after a false start, seduced by apparently easy maths.

1. Camel Ali says:

Ditto

14. Jerry says:

Dear Jane, stay in school, study hard and forget this loser.

1. A Robot says:

It’s a hoax.

2. Trees do grow outward as well. But what Richard was referring to was how a tree gains height, not width.

3. … Oh, except that tree has also grown upwards as well. Oops.

15. Physicalist says:

I got the age , but I wasn’t sure about how Jim would feel. Glad he apologized.

16. Stuart says:

Well my second answer was correct. And it only took me about 6 hours to get to the second answer 😦

17. 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.

18. 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…

19. ph49 says:

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.

20. Jerry says:

I got it!

21. Cathy says:

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.

22. Berber Anna says:

Yay, got it. That was my ‘creepy real world answer’, and it’s better than the ‘weird puzzle world answer’, I guess.

23. Sohvan says:

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?

1. Berber Anna says:

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.

2. 1STBORN says:

the answer to the tree part is right, the terminal buds(end of branches)are the only place elongation cells divide to give the tree height.the cambium layer cells that surrounds the trunk, branches and roots (under bark) can only grow in diameter.the roots have root caps that also can elongate. .I.S.A. CERTIFIED ARBORIST.

24. Anonymous says:

I expected to argue about reasonable assumptions, but I found out that my answer was wrong and I like the real one. Nice!

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26. Colin Whelan says:

This puzzle about tree growth is wrong although I have always thought it to be correct. I can send you photos of two trees as proof of you are interested.

27. Colin Whelan says:

I have just visited some remote areas of Australia researching a book on the period 1890-1920.
In 1891 there was a great shearers strike in Aust and one shearer at Brookong Station stabbed his shears into a tree in disgust at being sacked. These shears remain embedded in the eucalyptus…..15 metres above the ground!
In 1915 a shearer near the town of Deniliquin signed up to join the army for the Great War. He stabbed his shears into a gum tree saying he’d get them when he returned. He was killed. The shears remain deeply embedded into the tree…13 metres high. In the last week I’ve photographed both trees! I have always believed that trees grow from the top but now I KNOW differently

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