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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 273 · 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 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 405 (c) 342 (d) 396
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 19 (b) 18 (c) 20 (d) 9
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 20 (b) 19 (c) 9 (d) 21
  4. 4.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
  5. 5.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) 22 (b) 69 (c) 66 (d) 198
  6. 6.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
  7. 7.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 61 (b) 70 (c) 52 (d) 62
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 18 (b) 20 (c) 19 (d) 8
  9. 9.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 141 (b) 142 (c) 150 (d) 132
  10. 10.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 537 (b) 528 (c) 538 (d) 430
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 20 (b) 18 (c) 8 (d) 19
  12. 12.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 424 (c) 414 (d) 423
  13. 13.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 118 (c) 117 (d) 108
  14. 14.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  15. 15.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) 21 (b) 6 (c) 18 (d) 54
  16. 16.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) 57 (c) 54 (d) 18
  17. 17.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 232 (b) 222 (c) 226 (d) 231
  18. 18.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) 292 (c) 330 (d) 321
  19. 19.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 634 (b) 633 (c) 494 (d) 624
  20. 20.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 218 (b) 219 (c) 210 (d) 220
  21. 21.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) 30 (c) 9 (d) 27
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 8 (d) 18
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 4 (b) 16 (c) 15 (d) 14
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 5 (b) 14 (c) 16 (d) 15
  25. 25.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) 48 (b) 51 (c) 144 (d) 16
  26. 26.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) 18 (b) 5 (c) 15 (d) 45
  27. 27.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 488 (b) 615 (c) 624 (d) 625
  28. 28.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 75 (b) 66 (c) 84 (d) 76
  29. 29.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) 45 (b) 126 (c) 42 (d) 14
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 52? (a) 4 (b) 3 (c) 5 (d) 6
  31. 31.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 4 (d) 10
  32. 32.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
  33. 33.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 526 (b) 525 (c) 422 (d) 516
  34. 34.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 217 (c) 216 (d) 207
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 20 (b) 19 (c) 9 (d) 21
  36. 36.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 580 (c) 458 (d) 570
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 92? (a) 21 (b) 9 (c) 19 (d) 20
  38. 38.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  39. 39.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 5 (d) 14
  40. 40.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10

Answer key

  1. 405
  2. 19
  3. 20
  4. 8
  5. 66
  6. 2
  7. 61
  8. 19
  9. 141
  10. 537
  11. 19
  12. 423
  13. 117
  14. 7
  15. 18
  16. 54
  17. 231
  18. 330
  19. 633
  20. 219
  21. 27
  22. 18
  23. 15
  24. 15
  25. 48
  26. 15
  27. 624
  28. 75
  29. 42
  30. 5
  31. 3
  32. 30
  33. 525
  34. 216
  35. 20
  36. 579
  37. 20
  38. 2
  39. 6
  40. 9

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