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?

The owner of a popular clothing store comes up with his own method of pricing items. A vest costs $8, socks cost $10, a tie costs $6, and a blouse costs $12. Using the owner’s method, how much would a pair of underwear cost?

In a basket of apples,
when counted in twos, there was one extra
when counted in threes, there were two extra when counted in fours, there were three extra
when counted in fives, there were four extra
when counted in sixes, there was five extra.

However, if the apples were counted in sevens, no extra apple was left. Can you calculate the minimum number of apples that were present in the basket?

The dirtier I get, the whiter I look. Who am I?

Four men were in a boat on the lake. The boat turns over, and all four men sink to the bottom of the lake, yet not a single man got wet! Why?

You have two buckets - one holds exactly 5 gallons and the other 3 gallons. How can you measure 4 gallons of water into the 5 gallon bucket?

(Assume you have an unlimited supply of water and that there are no measurement markings of any kind on the buckets.)

Can you decipher the below rebus?

PBLUESAISNUERSES

A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 10 matches are played in total, how many players participated?
(b) If 20 players took part in the tournament, how many matches were played?

Can you solve the below algebraic mathematical equation?

(J+O+I+N+T)3 = JOINT

The centre of the third figure is empty. What digit should fit inside?