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

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!

C and F independently are connected to all except one circle. So, C and F cannot have two adjacent numbers. So C is 1 and F is 8. So A is 7 and H is 2.

3,4,5,6 needs to be placed in B,D,E,G

B and D cannot be 6

E and G cannot be 3

Since the image is symmetric across vertical line, lets say B is 3. If E is 6, and D and G become 4 and 5 which is not possible. So G is 6. So D is 4 and E is 5.

So, A is 7, B is 3, C is 1, D is 4, E is 5, F is 8 and G is 6.

Hope you all enjoyed the puzzle!