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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 83 · 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 two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
  2. 2.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 261 (c) 271 (d) 270
  3. 3.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 259 (b) 244 (c) 249 (d) 258
  4. 4.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) 30 (d) 9
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 19 (b) 8 (c) 18 (d) 17
  6. 6.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) 17 (c) 51 (d) 54
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  8. 8.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 378 (c) 330 (d) 387
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 16 (b) 17 (c) 18 (d) 6
  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) 39 (c) 117 (d) 13
  12. 12.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) 69 (b) 22 (c) 66 (d) 198
  13. 13.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 18 (c) 5 (d) 15
  14. 14.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  15. 15.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 240 (c) 238 (d) 249
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 20 (b) 9 (c) 19 (d) 21
  17. 17.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  18. 18.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 131 (c) 132 (d) 122
  19. 19.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) 14 (b) 126 (c) 45 (d) 42
  20. 20.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) 11 (c) 36 (d) 99
  21. 21.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 556 (c) 546 (d) 555
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 15 (b) 13 (c) 14 (d) 4
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 21 (b) 19 (c) 20 (d) 9
  24. 24.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  25. 25.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 460 (c) 583 (d) 573
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 4 (b) 3 (c) 2 (d) 5
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 4 (b) 5 (c) 2 (d) 3
  28. 28.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  29. 29.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 62 (c) 53 (d) 44
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 96? (a) 9 (b) 21 (c) 19 (d) 20
  31. 31.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 350 (c) 418 (d) 417
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 9 (b) 20 (c) 18 (d) 19
  33. 33.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 49 (b) 50 (c) 58 (d) 40
  34. 34.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 167 (b) 168 (c) 158 (d) 176
  35. 35.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  36. 36.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 159 (c) 168 (d) 150
  37. 37.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 447 (c) 370 (d) 448
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 16 (b) 6 (c) 18 (d) 17
  39. 39.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 609 (c) 619 (d) 618
  40. 40.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 71 (c) 80 (d) 62

Answer key

  1. 5
  2. 270
  3. 258
  4. 27
  5. 18
  6. 51
  7. 2
  8. 387
  9. 17
  10. 450
  11. 39
  12. 66
  13. 15
  14. 4
  15. 249
  16. 20
  17. 3
  18. 131
  19. 42
  20. 33
  21. 555
  22. 14
  23. 20
  24. 9
  25. 582
  26. 4
  27. 4
  28. 5
  29. 53
  30. 20
  31. 417
  32. 19
  33. 49
  34. 167
  35. 7
  36. 159
  37. 447
  38. 17
  39. 618
  40. 71

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