Can you align all of the coins on the right edge of the board?
The diagram above shows a 3 by 4 grid with 3 coins, one per row and one per column, such that the rightmost column of the grid is empty.
You are allowed to slide the coins to the columns on their right, but the coins can never leave the board (nor can they be moved back to the left). Also, you always have to move two coins at a time.
Thus, this is a legal move:
But moving a single coin, such as in the diagram below, is not allowed:
Your objective is to reach this position:
Can you do it?
What if you extend the board two columns to the left and two rows up, and add another two coins along the diagonal?
Give it some thought!
This is an adaptation of a problem from the book “Algorithmic Puzzles” by Anany Levitin and Maria Levitin.^{1}
Congratulations to the ones that solved this problem correctly and, in particular, to the ones who sent me their correct solutions:
Know how to solve this? Join the list of solvers by emailing me your solution!
You can move all coins to the right in 3 moves:
This diagram shows the evolution of the grid:
X . . . start
. X . .
. . X .
. X . . >
. X . .
. . . X >
. . X . >
. . X . >
. . . X
. . . X >
. . . X >
. . . X
If we extend the board up and left, we'd have this starting configuration:
X . . . . .
. X . . . .
. . X . . .
. . . X . .
. . . . X .
Now, consider the total number of spaces to the right of the coins:
X 1 2 3 4 5
. X 6 7 8 9
. . X 0 1 2
. . . X 3 4
. . . . X 5
We see that there are 15 spaces on the grid to the right of coins. We also know that each time we move two coins, the number of spaces to the right of the coins decreases by 2. Now, if we were to align all coins on the rightmost column, the number of spaces to the right of the coins would be 0. However, we can't go from 15 to 0 in decrements of 2, so with the extended setup it is impossible to solve the puzzle.
Don't forget to subscribe to the newsletter to get bi-weekly problems sent straight to your inbox.
This is an Amazon Affiliate link and I may earn a commission if you purchase the book. This comes at no extra cost to you. ↩
+35 chapters. +400 pages. Hundreds of examples. Over 30,000 readers!
My book “Pydon'ts” teaches you how to write elegant, expressive, and Pythonic code, to help you become a better developer. >>> Download it here 🐍🚀.