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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 817 · 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.

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  1. 1.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 175 (c) 176 (d) 166
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 46? (a) 13 (b) 4 (c) 12 (d) 11
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  4. 4.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  5. 5.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 126 (c) 116 (d) 125
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 50? (a) 6 (b) 3 (c) 5 (d) 4
  7. 7.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) 18 (c) 57 (d) 54
  8. 8.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
  9. 9.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 434 (b) 544 (c) 543 (d) 534
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 4 (b) 15 (c) 14 (d) 13
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 9 (b) 3 (c) 11 (d) 10
  12. 12.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 124 (c) 134 (d) 133
  13. 13.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 15 (d) 5
  14. 14.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 7 (b) 19 (c) 17 (d) 18
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 20 (b) 21 (c) 19 (d) 9
  17. 17.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 567 (c) 576 (d) 577
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 19 (b) 8 (c) 20 (d) 18
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 4 (b) 3 (c) 5 (d) 2
  20. 20.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) 69 (b) 72 (c) 207 (d) 23
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 5 (b) 4 (c) 3 (d) 2
  22. 22.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 73 (c) 82 (d) 64
  23. 23.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 295 (c) 294 (d) 285
  24. 24.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 103 (c) 104 (d) 112
  25. 25.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) 72 (c) 216 (d) 75
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 93? (a) 9 (b) 18 (c) 19 (d) 20
  27. 27.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 165 (c) 156 (d) 174
  28. 28.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 152 (c) 160 (d) 151
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 18 (b) 20 (c) 9 (d) 19
  30. 30.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 143 (b) 152 (c) 144 (d) 134
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 18 (b) 17 (c) 7 (d) 19
  32. 32.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 108 (c) 126 (d) 117
  33. 33.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) 15 (b) 45 (c) 48 (d) 135
  34. 34.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 337 (b) 336 (c) 296 (d) 327
  35. 35.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 124 (c) 132 (d) 123
  36. 36.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 463 (b) 380 (c) 462 (d) 453
  37. 37.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) 90 (b) 30 (c) 10 (d) 33
  38. 38.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 528 (b) 537 (c) 538 (d) 430
  39. 39.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 643 (b) 500 (c) 642 (d) 633
  40. 40.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 471 (b) 392 (c) 480 (d) 481

Answer key

  1. 175
  2. 12
  3. 5
  4. 2
  5. 125
  6. 5
  7. 54
  8. 27
  9. 543
  10. 14
  11. 10
  12. 133
  13. 5
  14. 4
  15. 18
  16. 20
  17. 576
  18. 19
  19. 4
  20. 69
  21. 4
  22. 73
  23. 294
  24. 103
  25. 72
  26. 19
  27. 165
  28. 151
  29. 19
  30. 143
  31. 18
  32. 117
  33. 45
  34. 336
  35. 123
  36. 462
  37. 30
  38. 537
  39. 642
  40. 480

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