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Grade 12 Challenge: Number Theory & Secret Codes Worksheet with Answers

Grade 12 (US) · Year 13 (UK) · Class 12 (India) · Math

Unit 6: Going FurtherReal-World ChallengesChallenge

Modular arithmetic at work: card and ISBN check digits, toy RSA keys, last digits of huge powers and calendar puzzles. This free high school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

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Challenge: Number Theory & Secret Codes

Grade 12 · Math

Score___ / 12

Name

Class

Date

Learning goal: Real-World Challenges

Directions: Solve each problem. Show your work, then write your answer in the box.

Example

Today is Friday. What day of the week will it be 2^20 days from today?

Answer: Tuesday

  1. 1

    ISBN-13 check digit: multiply the first 12 digits alternately by 1 and 3, add them up, and the check digit makes the total a multiple of 10. What is the check digit of 978-746594446-_ ?

    Show your work
    Answer
  2. 2

    Today is Thursday. What day of the week will it be 2^53 days from today?

    Show your work
    Answer
  3. 3

    How many positive whole numbers divide exactly into 3600?

    Answer
  4. 4

    Card numbers end with a Luhn check digit. What check digit completes the (made-up) card number 4622 7397 9800 450_ ?

    Show your work
    Answer
  5. 5

    What are the last two digits of 3^699?

    Answer
  6. 6

    How many positive whole numbers divide exactly into 810?

    Answer
  7. 7

    ISBN-13 check digit: multiply the first 12 digits alternately by 1 and 3, add them up, and the check digit makes the total a multiple of 10. What is the check digit of 978-590881336-_ ?

    Show your work
    Answer
  8. 8

    ISBN-13 check digit: multiply the first 12 digits alternately by 1 and 3, add them up, and the check digit makes the total a multiple of 10. What is the check digit of 978-311792064-_ ?

    Show your work
    Answer
  9. 9

    What are the last two digits of 19^144?

    Answer
  10. 10

    Toy RSA: p = 5, q = 13, so n = 65 and φ(n) = 48. The public exponent is e = 5. Find the private key d (0 < d < 48) with e·d ≡ 1 (mod 48).

    Show your work
    Answer
  11. 11

    Card numbers end with a Luhn check digit. What check digit completes the (made-up) card number 4337 5624 4226 301_ ?

    Show your work
    Answer
  12. 12

    Today is Saturday. What day of the week will it be 2^49 days from today?

    Show your work
    Answer

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Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/12/challenge_number_codes

Answer key (click to show)
  1. 1.9
  2. 2.Monday
  3. 3.45
  4. 4.6
  5. 5.67
  6. 6.20
  7. 7.5
  8. 8.5
  9. 9.21
  10. 10.29
  11. 11.3
  12. 12.Monday

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Does this Grade 12 Challenge: Number Theory & Secret Codes worksheet come with answers?

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