this month, Stage 3 & 4

January 1997

 

Problems

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14 Divisors

Stage:3 Challenge Level:Challenge Level:2Challenge Level:2

What is the smallest number with exactly 14 divisors?

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Pair Sums

Stage:3 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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Pythagorean Triples

Stage:3 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

How many right-angled triangles are there with sides that are all integers less than 100 units?

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Hockey

Stage:3 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

After some matches were played, most of the information in the table containing the results of the games was accidentally deleted. What was the score in each match played?

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Triangle Mid Pts

Stage:4 Challenge Level:Challenge Level:1

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?