Worksheets — Set 12

Number theory · Diophantine equations and cryptography

Print and write your answers. Use diagrams to show thinking.

Warm-up

1. How many subsets does a set with 16 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 15 fair tosses) = ___

_See printable PDF for diagram._

Written practice

1. How many subsets does a set with 15 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 14 fair tosses) = ___ 4. Write the recurrence aₙ = 14aₙ₋₁ with a₀ = 1 ___ 5. Graph with 16 vertices — minimum edges for connectivity? ___ 6. Convert 54₁₀ to base 15. = ___ 7. How many subsets does a set with 18 elements have? ___ 8. P(at least one head in 17 fair tosses) = ___

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More written practice

1. Write the recurrence aₙ = 17aₙ₋₁ with a₀ = 1 ___ 2. Graph with 19 vertices — minimum edges for connectivity? ___ 3. Convert 57₁₀ to base 18. = ___ 4. How many subsets does a set with 21 elements have? ___ 5. P(at least one head in 20 fair tosses) = ___ 6. Write the recurrence aₙ = 20aₙ₋₁ with a₀ = 1 ___

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Patterns and rules

1. How many subsets does a set with 32 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 31 fair tosses) = ___

_See printable PDF for diagram._

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Parent tip: Use trees or tables for counting