1998 PMWC Problems

Problem I1

Calculate:

Solution

Problem I2

Solution

Problem I3

Solution

Problem I4

Suppose in each day on a certain planet, there are only 10 hours and every hour has 100 minutes. What is the measure, in degrees, of the acute angle formed by the hour hand and the minute hand at 6 o'clock 75 minutes?

Solution

Problem I5

There were many balls which were distributed into 1998 boxes and all these boxes were arranged in a row. If the second box from the left-hand contained 7 balls and any 4 consecutive boxes always had a total of 30 balls, how many balls were there in the right-hand box?

Solution

Problem I6

After a mathematics test, each of the 25 students in the class got a quick look at the teacher’s grade sheet. Each student noticed five A’s. No student saw all the grades and no student saw her or his own grade. What is the minimum number of students who scored an A on this test?

Solution

Problem I7

Solution

Problem I8

A boy arranges three kinds of books which are 30 mm, 24 mm, and 18 mm thick, respectively. He places only books of the same thickness into 3 stacks of equal height, and wants to make the height as small as possible. How many books would be used in this arrangement?

Solution

Problem I9

How many triangles are there with side lengths whole numbers and with a perimeter of 10 cm ?

Solution

Problem I10

Find the number of factors of 960.

Solution

Problem I11

What is the units digit of ?

Solution

Problem I12

Solution

Problem I13

Every year there is at least one Friday the thirteenth, but no year has more than three. This year there are exactly three : in February, March and November. When will the next year be that contains exactly three Friday the thirteenths?

Solution

Problem I14

Solution

Problem I15

Construct a rectangle by putting together nine squares with sides equal to 1, 4, 7, 8, 9, 10, 14, 15 and 18. What is the sum of the areas of the squares on the 4 corners of the resulting rectangle ?

Solution

Problem T1

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Problem T2

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Problem T3

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Problem T4

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Problem T5

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Problem T6

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Problem T7

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Problem T8

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Problem T9

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Problem T10

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