Sujoy Kumar Datta

A cycling park has two identical circular tracks touching each other, and a rectangular track enclosing the two circles. The edges of the rectangles are tangential to the circles. Two friends, A and B, start cycling simultaneously form the point where one of the circular tracks touches the smaller side of the rectangular track. A cycles along the rectangular track, while B cycles along the two circular tracks in a figure of eight. Approximately, how much faster than A does B have to cycle, so that they take the same time to return to their starting point?

In how many ways can 18 sweets which are identical be distributed among 8 kids such that the number of sweets received by each kid is a prime number?

There are 43 A level and 51 B level players in a tournament. Each pair of A level players play one match. Each pair of B level players play one match. There is no match between A and B level players. The number of girl v. girl matches in A level is 120, while the number of boy v. boy matches in B level is 231. The total number of matches a girl plays against a boy is

If there are ten positive real numbers n1 < n2 < n3... < n10 , how many triplets of the form (n1, n2, n3), (n2, n3, n4), ... can be generated from the 10 numbers such that the first number is less than the second number, and the second number is less than the third number in each triplet?

In how many different ways can 9 identical balls be distributed among A, B, and C so that A gets at least 1 ball, B gets at least 2 balls, and C gets at least 3 balls?

There are 60 chairs around a round table. What is the least possible number of people sitting around the table if the next person to be seated around the table will have to sit next to someone?

Students in a college have to choose at least two subjects from chemistry, mathematics and physics. The number of students choosing all three subjects is 19, choosing mathematics as one of their subjects is 23 and choosing physics as one of their subjects is 26. The smallest possible number of students who could choose chemistry as one of their subjects is

85 children went on a school trip to an amusement park with three rides - merry go round, roller coaster, and Ferris wheel. Of them, 20 took all three rides and 55 took at least two of the three rides. Each ride cost $1, and in total $145 were spent on the rides. How many children took exactly one ride?

630 members of a group are arranged in rows for a group photo. Each row contains 3 fewer members than the row ahead of it. The number of rows that is not possible is