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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 725 · 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 3 written when you write all the numbers from 1 to 65? (a) 16 (b) 18 (c) 17 (d) 6
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 1 (b) 4 (c) 3 (d) 2
  3. 3.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 33 (b) 34 (c) 24 (d) 42
  4. 4.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 170 (c) 160 (d) 169
  5. 5.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 280 (c) 270 (d) 279
  6. 6.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 504 (b) 495 (c) 408 (d) 505
  7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 56? (a) 16 (b) 5 (c) 17 (d) 15
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 17 (b) 15 (c) 16 (d) 6
  9. 9.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 15 (d) 4
  10. 10.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
  11. 11.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 54 (c) 6 (d) 18
  12. 12.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) 369 (c) 379 (d) 324
  13. 13.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 12 (b) 10 (c) 11 (d) 4
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 13 (b) 4 (c) 15 (d) 14
  16. 16.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 633 (c) 494 (d) 634
  17. 17.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 64 (c) 73 (d) 74
  18. 18.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 63 (c) 54 (d) 72
  19. 19.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 296 (c) 337 (d) 336
  20. 20.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 312 (c) 322 (d) 286
  21. 21.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 24 (c) 27 (d) 8
  22. 22.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) 54 (b) 17 (c) 153 (d) 51
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 11 (b) 12 (c) 3 (d) 13
  24. 24.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 430 (c) 420 (d) 358
  25. 25.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) 30 (c) 9 (d) 81
  26. 26.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  28. 28.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  29. 29.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 77 (b) 78 (c) 86 (d) 68
  30. 30.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 12 (b) 39 (c) 108 (d) 36
  31. 31.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 57 (c) 171 (d) 19
  32. 32.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  33. 33.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 238 (c) 237 (d) 230
  34. 34.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 6 (b) 3 (c) 4 (d) 5
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 17 (b) 6 (c) 16 (d) 18
  37. 37.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) 216 (b) 24 (c) 72 (d) 75
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 7 (b) 19 (c) 18 (d) 17
  39. 39.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 361 (c) 351 (d) 312
  40. 40.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 96 (c) 78 (d) 87

Answer key

  1. 17
  2. 3
  3. 33
  4. 169
  5. 279
  6. 504
  7. 16
  8. 16
  9. 5
  10. 8
  11. 18
  12. 378
  13. 4
  14. 11
  15. 14
  16. 633
  17. 73
  18. 63
  19. 336
  20. 321
  21. 24
  22. 51
  23. 12
  24. 429
  25. 27
  26. 3
  27. 2
  28. 3
  29. 77
  30. 36
  31. 57
  32. 9
  33. 237
  34. 8
  35. 5
  36. 17
  37. 72
  38. 18
  39. 360
  40. 87

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