Why is 6 afraid of 7?

Can you place six X (crosses) in below board without making three in a row in any way ?

John speaks the truth only once a day in a week. Below are a few hints for you:

First: Days are Sunday, Monday and so on.
Second: One day he says, "I lie on Monday and Tuesday".
Third: On the next day, he says, "Today is either Thursday, Saturday or Sunday".
Fourth: On the next day, he says, "I lie on Wednesday and Friday".

Can you identify the day on which he speaks the truth?

Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

Two trains start at the same time, one from Bangalore to Mysore and the other from Mysore to Bangalore. if they arrive at their destinations one hour and four hours respectively after passing one another, how much faster is one train running than the other?

A Club organizes a Running Race, and John, Jacob, Minda, and Tony participated.

The results are as follows

John beats Jacob
Minda beats Toni
Toni beats John

Who came first in the race?

All of Jacob's shoes are red except two.
All of Jacob's shoes are green except two.
All of Jacob's shoes are yellow except two.

How many shoes does Jacob have?

How far can you walk into the woods?

John was going on a jungle trip. He asked his wife to pack something to eat, something to drink and something to burn if he feels cold in the jungle. When John opens the backpack he found just one thing in the bag. What was it?

One day, I thought of ways that can be used for creating a palindrome. So I decided that I will turn into a larger number by adding the reversed digits to the original number and keep doing it till I finally obtained a palindrome.

I am not sure if this process will always result in a palindrome eventually but I was able to produce a four-digit palindrome. Can you guess my starting number?