The Creative School of Maths and Music

Prove (by induction or otherwise) the product of r consecutive numbers is divisible by r!.

Aryabhatta Inter-School Mathematics Competition Aryabhatta Inter-School Mathematics Competition named after Aryabhatta, India’s great contributor to

Going back on time....CSMM acknowledged !

CSMM is acknowledged. Feels nice

What will be remainder when N=10^10+ 10^100 + 10^1000+ 10^10000..........+10^10000000000 is divided by 7?

100 coins are scattered on a table in a dark room. 90 of them have heads facing up and 10 of them have tails up. All the coins feel the same i.e you cannot distinguish between the heads or tails by feeling the coins.
How would you sort the coins into two piles (which might have unequal sizes) so that there are an equal number of tails in each pile?

A boy took a seven digit number ending in 9 and raised it to an even power greater than 2000. He then took the number 17 and raised it to a power which leaves the remainder 1 when divided by 4. If he now multiplies both the numbers, what will be unit's digit of the number he so obtains?

A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. Then the time required by the first pipe is?

Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 100 players took part in that tournament.

How many matches were played?

If in a tournament there are 8 teams, and each team plays the other twice. For a win, one point is awarded. No points are awarded/deducted for a loss. Draws are not allowed. What is the minimum number of points a team should secure to ensure that they reach the semifinals(next round)?

Boxes numbered 1, 2, 3, 4 and 5 are kept in a row, and they which are to be filled with either a red or a blue ball, such that no two adjacent boxes can be filled with blue balls. Then how many different arrangements are possible, given that all balls of a given colour are exactly identical in all respects?

In a locality, there are ten houses in a row. On a particular night a thief planned to steal from three houses of the locality. In how many ways can he plan such that no two of them are next to each other?