MathMoondoo

(math31) (হারা-ফেরা) হারাধনের দশটা হারানো ছেলে আবার ফিরে আসবে। বছরে একটা করে আসতে পারে - প্রথমে ৭নং এলো তারপর ৩নং তারপর ১নং ... এভাবে; কিংবা, প্রথম বছরে এলো ৩নং আর ১০নং, পরের বছরে এলো বাকি সবাই...এভাবে; ... ইত্যাদি নানা ভাবে। মোট কতভাবে দশটা ছেলে ফিরতে পারে?

(math30) There are 10 balls - 2 identical red balls, 3 identical green balls and 5 identical blue balls. In how many ways you can keep all the 10 balls in 6 distinct boxes so that each box gets at least one ball?

(math29) A Greek boy ends up writing the letter theta whenever he tries to write 0. If he writes all the integers 1 through 100000 then how many thetas does he write?

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(math28) A boy watches television daily in whole hours but with a quota of at most 11 hours in a week. Prove that on some consecutive days he watches exactly 20 hours in total.

(math27generalised) A toffee shop gives k toffees free for every m toffee-wrappers. If you buy n toffees then in total how many toffees do you get?

(math27) (free for three) A toffee shop gives a toffee free for every three toffee-wrappers. So if you buy 9 toffees then on giving back the wrappers repeatedly you end up eating 13 toffees in total.
If a shop gives a toffee for every m toffee-wrappers and you buy n toffees then in total how many toffees do you get?

(math25) Find the general term of the sequence 1,2,3,-4,-5,-6,7,8,9,-10,-11,-12, 13,14,15,... (alternate signs in block of three)

(math25) How many distinct terms are there in the expansion of (1+x^2+x^3)^20?

(math24) How many ordered pairs (x,y) of positive integers x, y are there such that the lcm of x, y is 1440?

(math23) The sum of 8 positive integers is 20. Prove that one is 4 or the sum of some is 4.