Friday 30 November 2012


Tomas Lindén’s IPP32 exchange was a devilish little puzzle designed by Vesa Timonen. Consisting of only two flat pieces of wood, the goal is to make a single, symmetric shape... Tomas kindly gave me a copy of his exchange puzzle and it has taunted me for the last few months – it is evil! Be warned!!
I had a quick bash at it while I was at IPP, and got nowhere...

Then I tried it while I was on holiday in NYC, and got nowhere...

Back at home, I put it on the vast shelf-of-puzzles-to-be-solved, and every now and then I’d take it down and fiddle around with it, and get nowhere...

During MPP7 several folks played around with it, and solved it, and I gave it another bash, and got nowhere... 

(Let me know if you aren’t sure where this one’s heading!)

OK, how hard can it be? You have two flat pieces that are virtually identical, and you’re told that they both need to be flat on the table and you have to make a symmetric shape.

At one point on my journey with this puzzle I found myself trading emails with Tomas, and making sure that he really meant both pieces literally flat on the table (yip!) and that it wasn’t some sneaky answer that relied on negative space (nope!) – this time (!) it really was a straight forward solution (hard to picture given this was the same guy that bought us the Black or White!)

Straight-forward it might be – simple it is not!

At one point I resorted to a feeble attempt at using some arithmetic, and measured the edges and played around with various sums and differences, trying to work out which bits needed to be combined or aligned to result in symmetric remainders ... and failed miserably. 

Some helpful soul mentioned that he’d eventually found the solution and then realised that he’d seen that shape a few times before, and not recognised the symmetry in the shape – GREAT! Now I know I’m going to kick myself when I eventually find the solution!

Months later, I found myself out and about having dinner with a bunch of puzzlers in The Hague, and this puzzle’s been doing the rounds and I’m literally the only one left who hasn’t solved it yet, so they give it to me and I try (yet) again! 


...and eventually one of them takes pity on me and shows me the answer, and my first reaction is “That’s NOT symmetrical!” – only it IS ... but until you ‘see’ it, you’ll be convinced it isn’t, and merrily move on to the next experiment.

For me, this has to be one of the best little bits of puzzling value for money (even if I HAD paid for it!) around at the moment ... I’ve heard stories of one or two gifted puzzlers finding the solution in mere seconds, but most folks take a decent amount of time to work it out ... and some of us took forever! 

Be warned – it is evil. But if you really do want one, I'm sure Tomas will sell you one over here...


  1. I was one of those lucky solvers. I Sussex it out at IPP while my exchange partner was solving WIL's "exchange". (Which I still haven't solved)

    Since that initial fluke, I've not managed this one again. Another puzzle for testing time I think. Thanks for the reminder!

  2. It's not a packing puzzle! I might just have to get one of these! I suspect that blowing on it won't help either!


  3. Nice description, Allard! It convinces me that there are people who did have a harder time with this "just two pieces" puzzle. After not solving it initally, I put it away for some time. Then in a discussion with a puzzle friend via mail I tried to solve it again and got nowhere.

    I thought about "both pieces flat on the table" and with some free interpretation, I found the "solution" from your picture above. Of course Tomas confirmed that this is not the solution.

    One early morning after that, still half asleep, I found a nice symmetrical solution and it did not look like anything I had expected before. Maybe that is the state of mind you need for solving puzzles? :)

    1. Thanks Goetz - I know exactly what you mean and I've solved quite a few puzzles after I've left them alone for a while and then had a brainwave while I was asleep, or in the shower (or both!) - allard

  4. It is unusual.... I was one of those lucky solvers also. I didn’t find this one terribly hard but have struggled terribly with a packing puzzle recently! Great puzzle to give out for others to play with!

  5. I struggled for about 2 hr. with no luck, but my son Steven of 25 years came back to me with the correct solution in 30 min. I am very proud of him because I am normally very good of solving puzzle. A little hint, it looks like a sign you have seen before.

  6. Hi Allard,
    I'm trying to understand what the word symmetric(k) even means. Is it mirror symmetry or just such that a line separates it into two congruent pieces? Thanks,

  7. Aha! figured it out. Really awesome puzzle!