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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 691 · 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.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) 176 (c) 175 (d) 166
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 52? (a) 5 (b) 6 (c) 3 (d) 4
  3. 3.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  4. 4.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 487 (b) 477 (c) 396 (d) 486
  5. 5.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 609 (c) 484 (d) 619
  6. 6.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 7 (d) 9
  7. 7.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) 372 (c) 363 (d) 373
  8. 8.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 18 (b) 6 (c) 17 (d) 16
  10. 10.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) 21 (d) 18
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 53? (a) 15 (b) 5 (c) 17 (d) 16
  12. 12.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 202 (b) 196 (c) 195 (d) 186
  13. 13.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 10 (d) 5
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 19 (b) 17 (c) 8 (d) 18
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 20 (b) 19 (c) 18 (d) 9
  16. 16.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 2 (d) 4
  17. 17.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) 81 (b) 27 (c) 9 (d) 30
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 6 (b) 3 (c) 5 (d) 4
  19. 19.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 198 (b) 66 (c) 69 (d) 22
  20. 20.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 136 (c) 118 (d) 127
  21. 21.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) 51 (d) 17
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 18 (b) 9 (c) 20 (d) 19
  24. 24.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 386 (b) 471 (c) 462 (d) 472
  25. 25.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 225 (c) 234 (d) 235
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 16 (b) 15 (c) 4 (d) 14
  27. 27.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 280 (c) 258 (d) 279
  28. 28.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 211 (b) 201 (c) 212 (d) 210
  29. 29.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) 72 (b) 207 (c) 23 (d) 69
  30. 30.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 613 (b) 603 (c) 612 (d) 480
  31. 31.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 279 (c) 264 (d) 289
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 7 (b) 5 (c) 8 (d) 6
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 17 (b) 15 (c) 5 (d) 16
  34. 34.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 246 (c) 255 (d) 242
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 9 (b) 21 (c) 20 (d) 19
  36. 36.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 9 (b) 19 (c) 20 (d) 21
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 94? (a) 19 (b) 9 (c) 21 (d) 20
  39. 39.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 31 (c) 22 (d) 32
  40. 40.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 361 (b) 312 (c) 351 (d) 360

Answer key

  1. 175
  2. 5
  3. 8
  4. 486
  5. 618
  6. 8
  7. 372
  8. 5
  9. 17
  10. 18
  11. 16
  12. 195
  13. 6
  14. 18
  15. 19
  16. 3
  17. 27
  18. 5
  19. 66
  20. 127
  21. 51
  22. 2
  23. 19
  24. 471
  25. 234
  26. 15
  27. 279
  28. 210
  29. 69
  30. 612
  31. 288
  32. 7
  33. 16
  34. 255
  35. 20
  36. 5
  37. 20
  38. 20
  39. 31
  40. 360

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