I didn’t add last week’s Classic to this blog, but I did produce a pretty graph in Jupyter from which you can read the right answer (in either graph, the point on the x-axis where the orange four-post line first exceeds the blue three-post line.)
This week’s Express is not difficult, but I did find the answer a little surprising.
I did this one analytically and by brute force simulation, and got the same answer with both methods. It’s in a github gist.
My answer last week seems to be wrong; I thought agreeing with LL would be enough. I will need to look more closely at it.
This week’s Classic is about stacking blocks. At first glance I thought it was Tower of Hanoi, but it’s a little different:
A fairly simple one this week, I think:
[W]hat is the longest word that doesn’t share any letters with exactly one state?
The word list is indicated, and “state” means a US state. It takes much longer to download the word list than to solve the first part of the problem!
EDIT: Nope! Not far wrong, but definitely wrong.
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!
EDIT 2: Revised the original spread sheet showing the rows that I had calculated wrongly, and producing a correct game state table.
Another week of being fairly confident about this week’s Riddler Classic. (Bolstered by getting exactly the right answer for the last one I did, if by a slightly inefficient method.)
The puzzle is a coin-picking game, with the usual aim of taking the last coins, but the unusual condition of having two coin stacks:
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.
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!