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Some problems

1)How many times is the digit 2 used when writing the numbers 1,2,.......,1000?

2) Define the special mean of two numbers x and y as the average of their Arithmetic mean and geometric mean. For how many x and y in the set {1,2,......,2016} is the special mean of x and y a perfect square?

3) Let N be an integer. Add the digits of N to get a smaller number. Repeat this process until you get a single digital number. For how many integers < 1000 is the final single digit number 5?

4) Find the maximum value of 6x-3y-8z subject to 2(x^2) +3(y^2)+4(z^2)=1.

5) Find the number of integers satisfying the following condition: [(x/100)•[x/100]]=5.

All these problems are from Pre RMO 2016 West Bengal region.

Note by Rakhi Bhattacharyya
8 months ago

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Can anybody give me the source for finding out the answer keys? Rakhi Bhattacharyya · 7 months, 4 weeks ago

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