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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 574 · 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.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 6 (b) 16 (c) 17 (d) 18
  2. 2.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 158 (c) 167 (d) 168
  3. 3.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 184 (c) 183 (d) 174
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 45? (a) 3 (b) 5 (c) 2 (d) 4
  5. 5.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 16 (d) 3
  6. 6.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 242 (c) 246 (d) 255
  7. 7.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 140 (c) 139 (d) 130
  8. 8.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 20 (c) 60 (d) 63
  9. 9.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 15 (c) 48 (d) 45
  10. 10.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10
  11. 11.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) 99 (b) 11 (c) 33 (d) 36
  12. 12.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 295 (b) 268 (c) 294 (d) 285
  13. 13.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 592 (c) 591 (d) 582
  14. 14.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 18 (b) 6 (c) 17 (d) 16
  16. 16.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 264 (c) 288 (d) 289
  17. 17.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 3 (d) 1
  18. 18.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 403 (c) 340 (d) 393
  19. 19.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 126 (c) 14 (d) 42
  20. 20.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 580 (b) 570 (c) 579 (d) 458
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 12 (b) 3 (c) 11 (d) 10
  22. 22.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 5 (d) 14
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 15 (d) 14
  24. 24.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 13 (b) 3 (c) 15 (d) 14
  26. 26.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 24 (c) 33 (d) 42
  27. 27.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  28. 28.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 108 (c) 100 (d) 99
  29. 29.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 361 (c) 360 (d) 312
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 4 (b) 3 (c) 1 (d) 2
  31. 31.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 5 (b) 4 (c) 7 (d) 6
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 4 (b) 5 (c) 3 (d) 2
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 75? (a) 7 (b) 14 (c) 13 (d) 11
  35. 35.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 493 (c) 483 (d) 492
  36. 36.The numbers 20 to 28 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) 216 (c) 72 (d) 75
  37. 37.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 7 (d) 8
  38. 38.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) 27 (b) 81 (c) 9 (d) 30
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 80? (a) 8 (b) 17 (c) 18 (d) 19
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 49? (a) 6 (b) 5 (c) 3 (d) 4

Answer key

  1. 17
  2. 167
  3. 183
  4. 4
  5. 4
  6. 255
  7. 139
  8. 60
  9. 45
  10. 6
  11. 33
  12. 294
  13. 591
  14. 9
  15. 17
  16. 288
  17. 2
  18. 402
  19. 42
  20. 579
  21. 11
  22. 6
  23. 15
  24. 7
  25. 14
  26. 33
  27. 3
  28. 99
  29. 360
  30. 3
  31. 2
  32. 6
  33. 4
  34. 13
  35. 492
  36. 72
  37. 8
  38. 27
  39. 18
  40. 5

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