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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 308 · 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.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) 33 (b) 10 (c) 90 (d) 30
  2. 2.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 624 (c) 634 (d) 494
  3. 3.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 45? (a) 4 (b) 5 (c) 3 (d) 2
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 10 (b) 12 (c) 4 (d) 11
  6. 6.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 11 (b) 12 (c) 13 (d) 5
  8. 8.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) 153 (c) 17 (d) 51
  9. 9.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  10. 10.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) 171 (b) 19 (c) 57 (d) 60
  11. 11.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 298 (c) 270 (d) 297
  12. 12.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 284 (c) 309 (d) 319
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 74? (a) 6 (b) 7 (c) 8 (d) 5
  14. 14.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 630 (b) 639 (c) 640 (d) 498
  15. 15.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) 33 (c) 24 (d) 42
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 7 (b) 18 (c) 17 (d) 19
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 18 (b) 19 (c) 20 (d) 8
  18. 18.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 42 (c) 39 (d) 117
  19. 19.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) 162 (b) 57 (c) 54 (d) 18
  20. 20.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 356 (b) 426 (c) 427 (d) 417
  21. 21.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) 48 (b) 45 (c) 15 (d) 135
  22. 22.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 320 (b) 363 (c) 372 (d) 373
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 13 (b) 4 (c) 15 (d) 14
  24. 24.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 508 (b) 410 (c) 507 (d) 498
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 9 (d) 20
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 56? (a) 6 (b) 3 (c) 5 (d) 4
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 15 (b) 14 (c) 16 (d) 4
  28. 28.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) 42 (b) 14 (c) 126 (d) 45
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 19 (d) 18
  30. 30.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 326 (c) 382 (d) 372
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 20 (b) 19 (c) 18 (d) 8
  32. 32.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 601 (b) 600 (c) 591 (d) 472
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 18 (b) 6 (c) 16 (d) 17
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 84? (a) 20 (b) 8 (c) 18 (d) 19
  35. 35.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 6 (d) 13
  36. 36.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 112 (c) 121 (d) 122
  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) 24 (b) 216 (c) 75 (d) 72
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 6 (b) 4 (c) 5 (d) 3
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 18 (b) 17 (c) 16 (d) 7
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 65? (a) 18 (b) 16 (c) 6 (d) 17

Answer key

  1. 30
  2. 633
  3. 6
  4. 4
  5. 11
  6. 3
  7. 12
  8. 51
  9. 3
  10. 57
  11. 297
  12. 318
  13. 7
  14. 639
  15. 33
  16. 18
  17. 19
  18. 39
  19. 54
  20. 426
  21. 45
  22. 372
  23. 14
  24. 507
  25. 20
  26. 5
  27. 15
  28. 42
  29. 19
  30. 381
  31. 19
  32. 600
  33. 17
  34. 19
  35. 7
  36. 121
  37. 72
  38. 5
  39. 17
  40. 17

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