1. The cost of 5 apples, 5 pears and one orange is 78 cents, when the cost of one apple, 5 pears and 5 oranges is 1 dollar and 18 cents. What is the cost of one pear? (All oranges are alike as well as pears and apples.)
2. What is the smallest number divisible by each of the numbers 1 to 20?
3. If you multiply all integers from 1 to 100 (1 and 100 included), you will get a large number ending in a lot of zeros. Exactly how many zeros will be at the end of this number?
4. Is it possible to fill in a 5x5 table using numbers such that the sum of all them is positive, but the sum of any 4 numbers forming a 2x2 sub-table is negative?
5. There are 32 students in the Math Club. In November one of them solved 15 problems while others solved less than that. Prove that there are at least 3 students who solved equal number of problems.
