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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 745 · 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 9 written when you write all the numbers from 1 to 37? (a) 3 (b) 1 (c) 2 (d) 4
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 15 (b) 13 (c) 14 (d) 4
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 18 (b) 19 (c) 17 (d) 7
  4. 4.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 89 (b) 98 (c) 80 (d) 90
  5. 5.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 331 (b) 321 (c) 330 (d) 292
  6. 6.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 502 (c) 501 (d) 406
  7. 7.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 360 (c) 361 (d) 351
  8. 8.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) 21 (c) 6 (d) 18
  9. 9.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 260 (b) 273 (c) 282 (d) 283
  10. 10.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 451 (c) 372 (d) 450
  11. 11.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) 42 (b) 13 (c) 39 (d) 117
  12. 12.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 7 (d) 9
  13. 13.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) 591 (c) 600 (d) 472
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 68? (a) 18 (b) 16 (c) 17 (d) 6
  15. 15.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 562 (c) 561 (d) 446
  16. 16.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 67 (b) 76 (c) 58 (d) 68
  17. 17.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 153 (c) 144 (d) 154
  18. 18.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) 9 (c) 81 (d) 27
  19. 19.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 96? (a) 21 (b) 19 (c) 9 (d) 20
  21. 21.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  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) 153 (b) 51 (c) 54 (d) 17
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 6 (b) 3 (c) 4 (d) 5
  24. 24.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) 207 (b) 72 (c) 69 (d) 23
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 16 (b) 18 (c) 6 (d) 17
  26. 26.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 268 (c) 267 (d) 250
  27. 27.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) 30 (d) 90
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 4 (b) 3 (c) 5 (d) 2
  29. 29.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 9 (d) 10
  30. 30.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 17 (b) 18 (c) 19 (d) 7
  32. 32.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
  33. 33.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 505 (b) 504 (c) 408 (d) 495
  34. 34.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 360 (c) 318 (d) 370
  35. 35.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) 33 (b) 99 (c) 11 (d) 36
  36. 36.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 288 (c) 270 (d) 297
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 2 (b) 1 (c) 4 (d) 3
  38. 38.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 5 (b) 2 (c) 3 (d) 4
  40. 40.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 330 (c) 298 (d) 340

Answer key

  1. 3
  2. 14
  3. 18
  4. 89
  5. 330
  6. 501
  7. 360
  8. 18
  9. 282
  10. 450
  11. 39
  12. 8
  13. 600
  14. 17
  15. 561
  16. 67
  17. 153
  18. 27
  19. 6
  20. 20
  21. 4
  22. 51
  23. 5
  24. 69
  25. 17
  26. 267
  27. 30
  28. 4
  29. 9
  30. 3
  31. 18
  32. 5
  33. 504
  34. 369
  35. 33
  36. 297
  37. 3
  38. 4
  39. 4
  40. 339

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