What is the fewest number of coins that would be required in order to make sure each and every coin touches exactly three other coins?

I have an apple tree , number of apple in this tree get doubles every week.

On 30th week , the tree gets completely filled with apples :-)



Can you tell me , on what week does my tree is half covered with apples ?

We have arranged an array of numbers below. What you have to do is use any kind of mathematical symbol you know excluding any symbol that contains a number like cube root. You can use any amount of symbols but you have to come up with a valid equation for all of them.

0 0 0 = 6
1 1 1 = 6
2 + 2 + 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

In front of you, there are 9 coins. They all look absolutely identical, but one of the coins is fake. However, you know that the fake coin is lighter than the rest, and in front of you is a balance scale. What is the least number of weightings you can use to find the counterfeit coin?

"That Restaurant always remains crowded. This is the reason why nobody goes there".

Can you find a flaw in this statement?

If we tell you that there is a relation between the numbers and letters in the given figure, can you analyze it and find the missing letter in the last box?

I sleep during the day and fly at night, but I have no feathers to aid my flight. What am I?

Can you find out what is missing?

1 3 5
2 4 ?

Hint: It's not six. Think out of the box.

What can run but never walk, have a mouth that never speaks, have a head that never weeps, and have a bed but never sleeps?

What do you think with the below Picture ?