Combinatorics | Number Theory Answers

If a three digit number is multiplied by 1001, it will be certainly divisible by three prime
numbers. What is their sum?

40 people are sitting around a table. Everyone noticed that one of the people sitting
beside him is wearing a dress of the same colour as him, but the other one was wearing a
dress of different colour. What is the number of different dress colours of those people?

A seven digit even number is divisible by 18. What will be the remainder if the sum of
its digits is divided by 9?

Average of 10 numbers is 121. The 11th number is 11. What is the average of these 11
numbers?

Only rickshaws and cars are allowed to move on a road. The total number of wheels on
that road is 17. What is the number of rickshaw on that road?

When Tanvir climbed the Tajingdong mountain, on his way to the top he saw it was raining 11 times. At
Tajindong, on a rainy day, it rains either in the morning or in the afternoon; but it never rains twice in the
same day. On his way, Tanvir spent 16 mornings and 13 afternoons without rain. How many days did it
take for Tanvir to climb the Tajindong mountain in total?

Subrata writes a letter to Ruponti every day (in successive intervals of 24 hours) from Korea. But Ruponti
receives the letters in intervals of 25 hours. What is the number of the letter Ruponti receives on the 25th

day?

How many solutions are there to the equation
x1 + x2 + x3 + x4 + x5 + x6 = 29
where xi; i = 1; 2; 3; 4; 5; 6; is a nonnegative integer such that
a) xi > 1 for i = 1, 2, 3, 4, 5, 6?

Out of 250 students who failed in an examination, it was revealed that 128 failed in mathematics, 87 failed in physics and 134 failed in chemistry. 31 failed in mathematics and physics, 54 failed in chemistry and mathematics, 30 failed in chemistry and physics. Find how many candidates failed in:
(a) In all the three subjects (7 marks)
(b) In mathematics but not in physics (2 marks)
(c) In chemistry but not in mathematics (2 marks)
(d) In physics but not in chemistry or in mathematics (2 marks)
(e) In chemistry or in mathematics but not in physics (2 marks)
Hint: Use venn diagram to simplify your work.

If the product of the digits of a number is a non-zero square number then the
number is called lucky number. How many three digit lucky numbers are there?