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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 560 · 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 2 written when you write all the numbers from 1 to 95? (a) 21 (b) 19 (c) 9 (d) 20
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 20 (b) 19 (c) 9 (d) 21
  3. 3.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) 8 (b) 24 (c) 72 (d) 27
  4. 4.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) 57 (b) 60 (c) 19 (d) 171
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 7 (b) 18 (c) 17 (d) 19
  6. 6.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 9 (b) 8 (c) 7 (d) 6
  8. 8.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 366 (c) 432 (d) 442
  9. 9.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  10. 10.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 525 (c) 535 (d) 428
  11. 11.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 2 (d) 1
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 58? (a) 6 (b) 5 (c) 7 (d) 4
  13. 13.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 83 (b) 74 (c) 92 (d) 84
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 54? (a) 15 (b) 17 (c) 16 (d) 5
  15. 15.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) 30 (b) 81 (c) 27 (d) 9
  16. 16.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 52 (c) 70 (d) 61
  17. 17.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 23 (b) 207 (c) 72 (d) 69
  18. 18.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) 54 (b) 6 (c) 18 (d) 21
  19. 19.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 470 (b) 598 (c) 597 (d) 588
  20. 20.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 128 (c) 119 (d) 110
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 8 (b) 20 (c) 19 (d) 18
  22. 22.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 253 (b) 240 (c) 243 (d) 252
  23. 23.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 380 (c) 463 (d) 453
  24. 24.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 173 (b) 174 (c) 164 (d) 182
  25. 25.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) 18 (c) 162 (d) 54
  26. 26.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 16 (b) 51 (c) 48 (d) 144
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 2 (b) 5 (c) 3 (d) 4
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 20 (d) 9
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 15 (b) 3 (c) 14 (d) 13
  30. 30.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 309 (b) 284 (c) 319 (d) 318
  31. 31.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) 90 (c) 30 (d) 10
  32. 32.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 459 (b) 460 (c) 378 (d) 450
  33. 33.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 90? (a) 18 (b) 20 (c) 9 (d) 19
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 15 (b) 17 (c) 16 (d) 5
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 8 (b) 11 (c) 9 (d) 12
  37. 37.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
  38. 38.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) 99 (c) 108 (d) 100
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 7 (b) 5 (c) 4 (d) 6
  40. 40.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 95 (b) 96 (c) 104 (d) 86

Answer key

  1. 20
  2. 20
  3. 24
  4. 57
  5. 18
  6. 6
  7. 8
  8. 441
  9. 4
  10. 534
  11. 2
  12. 6
  13. 83
  14. 16
  15. 27
  16. 61
  17. 69
  18. 18
  19. 597
  20. 119
  21. 19
  22. 252
  23. 462
  24. 173
  25. 54
  26. 48
  27. 4
  28. 20
  29. 14
  30. 318
  31. 30
  32. 459
  33. 6
  34. 19
  35. 16
  36. 11
  37. 7
  38. 99
  39. 6
  40. 95

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