My strategy of starting with the easy cases and building out to more complex cases was used successfully by other solvers. My analysis of the easy cases was correct, but there was a mistake in the way I built out. My diagram probably didn’t help; the one drawn by the winner didn’t distinguish between the larger and smaller piles, and I think that’s where my error crept in.
For example, when I considered (9, 5), I thought it was a losing position because I didn’t see that taking six coins from the larger pile produced (5, 3), since the larger pile became the smaller pile in that move. So the “simplification” I introduced, of specifying one pile as larger, while not wrong, made it easier for me to make a mistake. It helped to break my mental model by suggesting an identity for the piles (“larger” or “smaller”) that isn’t persistent, but depends on the progress of the game. Will try not to do that again!
This spread sheet is my own attempt to show how the collateral flow to or from a clearing house works. I created it about five years ago when I was working at a bank, and needed to explain the relationships between different quantities, and how they are calculated.
If you have a rough idea of how futures work, and want to see a detailed example, this post might help. If you don’t know what futures are, this won’t help, but Wikipedia’s intro might.
At the end of November last year, my girlfriend and I decided to try a diet box company. We chose wsmaq after trying one-day samples from them and one other company; the food from wsmaq was noticeably better.
Initially I thought this week’s Classic puzzle might be too tough to solve without some serious insights, but the more I thought about it, the more it seemed like I might be able to break it down to manageable pieces.
I’ve had this mental model for a while, but it solidified a year ago after explaining it at work, and I wanted to use it again in a Twitter debate shortly afterwards. Twitter’s the wrong place for real explanations though, so here it is.
This model will not solve your disagreements for you, and it’s not a substitute for calculating the NPV of your possible projects. Instead, it’s a quick shorthand that might make discussions more useful, and show you something about your team.
Last night, the betting markets were giving the Tories a better than 75% chance of winning a majority in Thursday’s general election. Polls still have them far ahead, and personally, I expect that they’ll do it.
If we are wrong about that, and they don’t form a majority, why might that be? If a hung parliament is coming, what would make people blind to it?
Most of the Classics look too difficult for me to be able to solve, but this week’s looked like I could approach it. No code required, either.
Here’s the question:
Five friends … are playing the … Lottery, in which each must choose exactly five numbers from 1 to 70. After they all picked their numbers, the first friend notices that no number was selected by two or more friends. Unimpressed, the second friend observes that all 25 selected numbers are composite (i.e., not prime). Not to be outdone, the third friend points out that each selected number has at least two distinct prime factors. After some more thinking, the fourth friend excitedly remarks that the product of selected numbers on each ticket is exactly the same. …
What is the product of the selected numbers on each ticket?
There might be a neat, elegant way of solving this, but I chipped away at it bit by bit.
Thought I’d see if I can get back into the groove of doing these, at least sometimes. This week‘s is geometry. I admit I got a bit of fear when I looked at it; geometry is something I haven’t used much since school, so it doesn’t come back so easily.
This week’s seems a little more involved than the Expresses usually are (although I’ll admit July 27th‘s really stumped me!):
Take a standard deck of cards, and pull out the numbered cards from one suit (the cards 2 through 10). Shuffle them, and then lay them face down in a row. Flip over the first card. Now guess whether the next card in the row is bigger or smaller. If you’re right, keep going.
If you play this game optimally, what’s the probability that you can get to the end without making any mistakes?
I got nowhere when I tried visualising this as a decision tree. Too wide and deep for me to understand it. Then I did the sensible thing, and broke it down into simpler problems. I also tried staying away from Excel for a while, a new one for me!