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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 653 · 40 questions
TalentJR

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

NameDateTime takenScore ___ / 40
  1. 1.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 588 (c) 464 (d) 589
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 16 (b) 14 (c) 5 (d) 15
  3. 3.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 10 (c) 33 (d) 90
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 20 (b) 21 (c) 9 (d) 19
  5. 5.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 7 (b) 8 (c) 9 (d) 6
  7. 7.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 17 (b) 8 (c) 19 (d) 18
  10. 10.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 149 (c) 150 (d) 158
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 97? (a) 20 (b) 21 (c) 9 (d) 19
  12. 12.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  13. 13.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 8 (b) 18 (c) 20 (d) 19
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 7 (b) 17 (c) 19 (d) 18
  16. 16.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 7 (d) 6
  17. 17.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 495 (c) 504 (d) 505
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 17 (b) 19 (c) 7 (d) 18
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 2 (b) 4 (c) 5 (d) 3
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 99? (a) 20 (b) 21 (c) 9 (d) 19
  21. 21.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 300 (c) 291 (d) 272
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 19 (b) 18 (c) 8 (d) 20
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 4 (b) 1 (c) 3 (d) 2
  24. 24.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
  25. 25.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 153 (b) 54 (c) 51 (d) 17
  26. 26.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 54 (c) 18 (d) 162
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  28. 28.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 168 (c) 178 (d) 177
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 19 (b) 20 (c) 21 (d) 9
  30. 30.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
  31. 31.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 9 (b) 81 (c) 27 (d) 30
  32. 32.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 36 (c) 11 (d) 99
  33. 33.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 528 (c) 537 (d) 538
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 18 (b) 17 (c) 19 (d) 7
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 81? (a) 8 (b) 18 (c) 17 (d) 19
  36. 36.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 324 (c) 369 (d) 379
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 80? (a) 17 (b) 8 (c) 19 (d) 18
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 6 (b) 4 (c) 5 (d) 7
  39. 39.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 73 (b) 82 (c) 64 (d) 74
  40. 40.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 63 (c) 21 (d) 7

Answer key

  1. 588
  2. 15
  3. 30
  4. 20
  5. 4
  6. 8
  7. 6
  8. 5
  9. 18
  10. 149
  11. 20
  12. 3
  13. 9
  14. 19
  15. 18
  16. 7
  17. 504
  18. 18
  19. 4
  20. 20
  21. 300
  22. 19
  23. 3
  24. 8
  25. 51
  26. 54
  27. 2
  28. 177
  29. 20
  30. 7
  31. 27
  32. 33
  33. 537
  34. 18
  35. 18
  36. 378
  37. 18
  38. 6
  39. 73
  40. 21

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