Plan an Unbeatable Strategy

Two people play a game of NIM. There are 100 matches on a table, and the players take turns picking 1 to 5 sticks at a time. The person who takes the last stick wins the game. (Both players has to make sure that the winner would be picking only 1 stick at the end) 

Who has a winning strategy?

And what must be winning strategy in the person who takes the last stick looses?

This could be the winning strategy! 

Planned The Unbeatable Strategy!

What is the game?

The first person can plan an unbeatable winning strategy.

CASE 1 : The person picking last stick is winner.

All that he has to do is pick 4 sticks straightaway at the start leaving behind 96 stick. Then, he has to make sure that the count of remaining stick will be always divisible by 6 like 96, 90, 84, 78......6. 

So if the opponent takes away 2 sticks in his first turn, then first person has to take 6 - 2 = 4 sticks leaving behind 90 sticks there. That is if the opponent takes away X stick the first person need to pick 6 - X sticks.

Now, when there are 6 stick left, even if opponent takes away 5 sticks then 1 stick will be left for the first person.

And even if the opponent picks 4 sticks then first person will take 2 remaining sticks.

CASE 2 : The person picking last stick is looser. 

Now the first person need to take away 3 sticks in first turn leaving behind 97. Next, he has to make sure the count of remaining sticks reduced by 6 after each of his turn. That is, the count should be like 91,85,79,72......7.

So if the opponent takes away 4 sticks in his first turn, then first person has to take 6 - 4 = 2 sticks leaving behind 91 sticks there. That is if the opponent takes away X stick the first person need to pick 6 - X sticks.

When there are 7 sticks are left then even if the opponent takes away 5 sticks then first person can force him to pick the last stick by picking only 1 stick of remaining 2. 

And if the opponent takes away 4 sticks at this stage, the first person still can force him to pick last stick by picking 2 of remaining 3 sticks.

Conclusion : The first person always has a chance to plan a winning strategy.

Squares From Squares Challenge

In the picture that is attached with this question, you can find a square which comprises of four little squares inside it. Consider this square to be made with matchsticks. You have to remove two matchsticks such that only two squares remain instead of five.How will you do it ?

Make it 2!

Challenge accepted here! 

Source 

Squares From Squares Challenge Accepted

What was the challenge? 

All that you need to do is that remove these 2 match sticks labelled in figure below.

So we get exactly 2 squares as below.

Remove Matches To Match Number

Remove six matches to make 10.

Shown here how it can be done!

  

Matches To Match Number

What was the challenge? 

It's pretty simple one. Nowhere it is mentioned that you have to make it as 

10 & not allowed to make TEN. So three sticks from first, one from second & 

2 from third gives us TEN.

However, we can make it as 10 as well. Removing 1 stick from first, 4 from 

second & 1 from third produces 10.