Interpreting and Evaluating - January 2009, Stage 3&4

This month our problems involve aspects of the process of interpreting the information in a question and examining in various ways the solution or methods used to get the solution. For example, are the assumptions and arguments made correct or appropriate? How does the solution relate to the initial problem? Can we make sense of someone else's finding? Can we compare strategies used?

Problems

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Elevenses

Stage: 3 Challenge Level: Challenge Level:1

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

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Remainders

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

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

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American Billions

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

Find the ten-digit number in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3, the first four digits make a number divisible by 4...

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Beelines

Stage: 4 Challenge Level: Challenge Level:1

Investigate the relationship between the coordinates of the endpoint of a line through the origin and the number of grid squares it crosses.

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Time to Evolve

Stage: 4 Challenge Level: Challenge Level:1

How many generations would link an evolutionist to a very distant ancestor?

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More or Less?

Stage: 4 Challenge Level: Challenge Level:1

Are these estimates of physical quantities accurate?

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Making Sixty

Stage: 4 Challenge Level: Challenge Level:1

Why does this fold create an angle of sixty degrees?

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Bendy Quad

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

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Partly Circles

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the same and what is different about these circle questions? What connections can you make?

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Napkin

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A napkin is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed .

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Why 24?

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Take any prime number greater than 3, square it, subtract one and divide by 24. Make a statement about what you notice about dividing by 24 (a conjecture) and prove that what you say is always true.

Elsewhere...