Twelve Coins

You have twelve gold coins, but one is a forgery. The forgery is lighter or heavier than the eleven true coins, but you do not know which. You have a pair of scales, in which you can weigh any combination of those coins against each other, but not against anything else. You can use the scales to weigh three combinations of coins. What combinations should you weigh, so that you will always be able to tell which is the forgery, and whether it is lighter or heavier than the others?

S told me that puzzle around 1990, and said she used it to get free drinks: in a week’s time she would buy the other a drink if he answered it, he would buy her one if he could not. I took four hours to work it out over two days, and it gave me intense joy. Leave a comment if you work it out.

There is a variant of Oware in which the second to move may always win, if she chooses the steps correctly. I have worked them out, and thought, it takes a special type of personality to enjoy that and be able to function in the world. Not now functioning, I think of that joy in pure intellectual puzzles. I am not using it for my advancement, but in Switzerland physicists have used the Large Electron Positron collider to work out what happened one billionth of a second after the Big Bang, and are now using the Large Hadron Collider to work out what happened in the second trillionth of a second. What is the use of that? Well, hospitals use particle accelerators to create unstable isotopes, which, ingested, produce positrons- antimatter- enabling the doctors to build up images of the brain as a diagnostic tool. This is called Positron Emission Tomography.

When S asks “what are the reasons why we should accept you as a woman?” Nicole says it is a matter of heart and soul, and indeed it is. (Read her post on Daniel, for goosebumps and tears.) And S, having worked through her anger at my barging into Women’s space, and found some liking for me, and still thinking, or feeling, that I am not really a woman, takes this intellectual, reasoning approach. I would rather she did, than surrender to anger. She may even, through reason, talk her own heart-response round.

I am glad to hear of her anger, because I did not feel anger from her, only withdrawal, and in that women’s space last year I felt apprehensive of anger. In January 2010 my ways of hardening myself to cope with the World finally broke down, and I am seeking all means to cope as my unprotected self.

I have played Solitaire obsessively, and this morning spent fifty minutes on one game, my 653rd, repeatedly making the moves and rewinding them to see what order the stack had to be distributed on the layout, and how to do that, to get it out- my 95th win. I found that satisfying, however empty I find my addiction to it normally. Whatever, it is worth spending time finding what delights me, and what, so like it, I falsely imagine delights me.

TEDx: Louie Schwartzberg on Gratitude, with some gorgeous images. Thanks to Jacqui.

5 thoughts on “Twelve Coins

  1. Clare,
    I always loved math, including calculus at University, but but word problems were/are my nemesis. Not even tempted by the one here. 🙂 but I appreciate the value of intellectual puzzles.

    Interestingly, your mention of PET Scanners takes me back to the early 80s when I worked as a research assistant at the University of Miami and helped with brain studies using one of the early PET scanners. Fascinating technology which takes advantage of a distinct property of positrons. That is, when they decay, they release two gamma particles exactly 180 degrees opposed which can then be detected by sensors in an array.

    And I do like your segueways from intellectual to personal. Always interesting.


    • Here, the question is, how do you classify the coins? How do you think of them after weighing? You have to get every bit of information from each weighing. I will integrate the intellectual and personal later, at the moment I am altering my relationship to both.


  2. Hmmm.

    If I knew if the forged coin was lighter or heavier, it would be easy — flor example, if the forged coin were heavier I’d: weigh six and six, then three and three of the six that was heavier; then pick any two out of that. If the last two are the same, the forged coin is the third. If the last two are different, the heavier one is the forgery.

    Not knowing if the forgery is heavier or lighter means I can’t necessarily do it in three moves. Hmmmmm.


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