Mother*****

(Before you accuse me of cursing, count the asterisks.)

Okay, so my computer seems to have a motherboard failure, since Tuesday. Which means I have had no computer access for three days, and depending on luck, I may or may not get computer access on IPC (7-9 July, aka 2 days). So…I might be solving by phone or something, depending on my mood and the eventual availability of my computer on the competition weekend. 😦

On a somewhat related note, no computer access makes me focus on solving puzzles and making them. I’ve solved Will Shortz’s Puzzlemaster Workout, with an average performance somewhere above expert time but definitely not record time (although I broke 19 record times, some of them in the “lucky” genres like Honey Islands and Boomerangs (I haven’t figured out a logical way to approach any of them, with brute force seeming to be the best method I found so far) but screwed up 5 puzzles). I’m catching up with Grandmaster Puzzles, and I might some time send some puzzles there; if I eventually send puzzles there, I already plan to send my vanilla and standard variant (is that an oxymoron?) puzzles to GMPuzzles and keep the more wicked variants for this blog. I’m making the second 7×7 Fillomino batch (the first is Fancy Fillomino February), which won’t be themed for a certain month but will be far more wicked than FFF. (Currently I’ve made Liar Cipher Fillomino and Consecutive Shikaku Fillomino, to give an idea of what puzzles I’m making. 😛 )

…alright, that’s all for now, I guess. Because it has been a long time since the last puzzle, let’s make a short one.

You have ten piles of coins, of sizes 1,2,3,4,5,6,7,8,9,10 (one pile each). You also have a pan. You can put any pile on the pan, but you must put all coins from the pile and no other coin from other piles. Design a sequence of piles and put the piles to the pan in that order, so that after any move, the total number of coins on the pan is not a prime number. There might be multiple sequences, but I’ve found at least one so this “puzzle” is solvable.

(An example sequence is 1,2,3,4,5,6,7,8,9,10, but it hits the prime 3 after two moves. Another sequence is 10,9,8,7,6,5,4,3,2,1, but it hits the prime 19 after two moves.)

If you found an answer, can you find one satisfying 1,_,3,_,5,_,7,_,9,_ where the underscores are to be replaced by the remaining numbers (2,4,6,8,10)?

What if you have 2013 piles whose sizes are the first 2013 positive integers instead? Can you find a way to construct the solution for any number of piles greater than or equal to 3 that always works (without trying too many possibilities of course)? (That is called a general solution.) Can you find a way to construct general solutions?

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2 thoughts on “Mother*****

    • It’s prime at the first step (3).

      But yeah, 1,3,2,4,5,6,7,…,n is a general solution, and it is the only general solution that tampers with the first three positive integers only. All other general solutions fix more than 3 positive integers (or otherwise are of different forms).

      Reply

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