Solution to Puzzle #186: 4×4 Grid

This was a simple puzzle, a classical application of the pigeon hole principle. I got correct answers from Deepak Goyal (my brother in NY), Mahi Saraf (as always) and Pratik Poddar (as always again).

I am taking the liberty of copying the answer from Mahi.

Part 1
There are multiple answers to this one. I am producing two one from Mahi, and another one from Deepak.
From Mahi:
The plus signs represent the squares with the dots and the ones with the underscore signs represent the empty squares
_ _ _ +
_ + + _
+ _ +  _
+  + _ _
From Deepak
Solution to Puzzle #186

Solution to Puzzle #186

Part 2
When we  arrange 6 stars in a 4 by 4 grid, by pigeon hole principle there will be at least one row with 2 stars so we strike that. If the row we chose had exactly 2 stars then there will be one more row with 2 stars so we strike that to. Now we will be left with 2 stars and 2 strikes hence, we can cut all the stars.
If the first row we chose had 3  stars then we will be left with three stars and 3 strikes so even in this case we will be able to strike out all stars.
The last possibility could be that the first row we chose had 4 stars in it so we will have 2 stars and 3 strikes remaining.
Therefore, We can never arrange 6 stars in a 4 by 4 grid so that by striking 2 rows and 2 columns we will still be left with 1 star.
Hope you all enjoyed the puzzle!
This entry was posted in Solution and tagged , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s