OK, here we go with this week’s teaser.

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?

As ever, please do NOT post your answers, but do say if you think you have solved the puzzle and how long it took.  Solution on Monday.

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.

92 comments

    1. You can’t sell your case. You can probably figure out the reason why — I don’t want to say it since it may offer a hint of sorts to those who haven’t yet solved the puzzle.

    1. Yeech. You’re right. Then again, if we’re to assume that she grows exactly 8 cm each year, every year, then this isn’t necessarily the most realistic of puzzles to begin with, so who can be exactly sure how Richard wants us to interpret it?

    2. It doesn’t say she grows, though, just that her reach extends. Maybe he provides her with a longer stick each year? 😛

    3. If it only said “she grew…” you’d ask – but what about her arms? I think its fair to say “her reach extends by 8cm / yr” to mean something like she got 4cm taller and her arms got 4 cm longer.

      And another thing! Til now everyone keeps talking about the girl or the tree….

  1. I think we haven’t been given enough information to answer the question definitively. The information given could allow for any answer between A and B, depending on what the other unstated variables are. A and B are very substantially different.

    1. I don’t think we can really work out the definitive answer unless we know whether Jim intended to marry Jane or not. I have created a BASIC program on my commodore 64 to go through all the variables and it conclusively proves that it is inconclusive.

  2. In order to answer we need to know at how much length Jim has craved the heart and total length of tree at the time of craving considering the tree will grow in equal proportion..

  3. Well there’s the obvious answer but it took a few seconds to realise that had some rediculous consequences so that left another answer But then another suposition occurred to me as I read the first comment. Now I seem to be in agreement with others here in less than a minute.

  4. It’s not an unrealistic puzzle. I also gain 8cm of reach every year. I could reach my dad’s nose when I was 8, now I can put my elbow in a basketball hoop. How old am I?

  5. There’s some missing information about the season when the puzzle happens. It could make a quite significant difference to the answer.

  6. As always there’s a twist in the tale… Thought I had it then realised I didn’t then discovered the key to the solution. There is one. It’s not hard.

  7. She had always been a happy child. That was, of course, before the Spurt.

    Her friends were astonished, her doctors; puzzled. Not only was she outgrowing her peers at a phenomenal pace, she was doing so at an eerily constant rate as well.

    “8 centimeters, every year, since the age of 8. No exceptions,’ Dr. Ramprakash muttered to himself, trying desperately to make sense of the unwaveringly linear graph propped up against the wall.

    Her Vietnamese parents were over the moon. For centuries, their bloodline had ensured that not a single individual had any reason to be annoyed be low-lying doorways. “We’re both very proud of Jane,” beamed her doting mother, “Finally, I don’t have to climb up on to the counter to reach the cumin.”

    Jane herself was less than enthused. “None of the boys will even look at me. I feel like some kind of a monster,” she scribbled in her diary, on the eve of her sixteenth birthday. She cried herself to sleep that night, the extremities of her 6 foot 3 inch frame dangling wearily off the edge of her bed.

    She’d never quite gotten over Jim either. “Maybe, just maybe”, she thought to herself on particularly malevolent days, “I’d have forgotten about him by now if he hadn’t made all those pathetic promises.” It didn’t help that his newly-wedded bride was a gorgeous, petite lady who she dreamed of crushing under her ridiculously large feet.

    Ramprakash had thrown in the towel over a year ago. In fact, not a single medical expert had the faintest intuition. Every scan, every test and every fancy-schmansy diagnostic machine had come up blank. Jane continued to grow, and wallow in woe.

    She died peacefully in anguish, some years later. Her sullen corpse, too large for a standard coffin, was left out for the vultures.

    Her story, sadly, has been resigned to near-obscurity. But every now and then it appears fleetingly on the interwebs; quoted by Wise men as riddles in a rather more watered-down context.

  8. A couple of minutes lateral thinking then a further reading of the question and an answer that I think I might be debating with others on Monday. My answer is very specifically influenced by what Jim promises! It requires no arboreal knowledge.

  9. 1 min to understand the question and draw a diagram.
    10 secs to come up with a mathematical answer.
    1 min to find a ‘real world’ (England and Wales) solution !

  10. 10 minutes of writing a simulation as a perl exercise and concluding that they will have a fine marriage.
    Then 3 hours wondering what I missed.
    2 minutes of reading comments.
    1 minute of facepalming.
    1 minute of rewriting the silly perl script just for spite.
    3 hours 14 minutes.

  11. A couple of seconds to do the primary school maths equation. A few more seconds (after reading the comments about tree growth) to realise I’d made an obvious error and revise it to something far more achievable (albeit causing a few legal problems!). A few more seconds to realise another fallacy with answer (1) – this time related to how humans grow…

    So…
    Answer 1) He’s got the patience of a saint
    Answer 2) Far quicker, but there’d be legal implications
    Answer 3) He’ll remain a batchelor for life, unless…
    Answer 4) She buys a chainsaw or there’s a hurricane 🙂

  12. At first I thought I got it straight away, then took a moment of going through the math equation I wrote down to realise my mistake. It’s quite funny to miss something that obvious 🙂

  13. Hmmmm…two answers. Not sure on the right one. If one of them is even right at all. Got it in 30 seconds. So probably both are wrong.

    1. I am profoundly ignorant about how trees grow, and so are probably most people in this thread. That’s what makes it interesting.

    2. Maybe John was just profoundly ignorant of how trees grow. He’ll have plenty of time to brush up on his botany from his jail cell.

  14. There is a second answer based on language semantics, but I find nit-picking grammar to be fairly lame as brain teasers go. Either way, Jim is still a pedo.

  15. Sounds like the exercise with the worm crawling out of the well, but while that one is tricky because of the discontinuity, I can’t decide if that applies here, too.

    I assume that trees only actually grow in part of the year, but I don’t know if human growth is continuous or not.

  16. Page 112 of the 7th edition (1989) of the Guinness Book of Answers says that the average 8-year-old girl grows from 77.5% of her eventual adult height to 80.7% in one year.

    Assuming that this annual growth of 3.2% is 8 centimetres, and assuming that Jane’s growth rate is the same (as a proportion of adult height) as the average girl, then Jane’s eventual adult height will be 2.50 metres (8′ 2½”), and at the age of 8 she is already 1.94 metres (6′ 4½”) tall. So how the **** tall is Jim already?

  17. Found quite a few answers escaping the riddle with silly answers, but I think I got the intended answer. My initial solving took a couple of minutes. Confirming via wiki took 10-15 minutes. I liked the puzzle 🙂

  18. Two solutions, one of which might involve the authorities depending on how tall the tree was when this started. About 1 minute to see the second.

    –Dave

  19. I know the answer, it took me a few minutes and I thought it would take me ages!
    By the way, I watched you on friday at the conference in London, it was amazing ( i was the first one to have a picture with you, in the checkered shirt haha) 🙂

  20. Took me about 10 seconds for my answer. Then I read the comments and realized the community of botanists was thinking the same as I was me.

  21. Depends on whether Jim could afford to get married after harming the tree, being fined under the relevant legislation, battling the EDO in court and having to restore several acres of land as recompense – sigh….
    Apart from that – a minute or so.

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