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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 92 · 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 2 written when you write all the numbers from 1 to 93? (a) 21 (b) 20 (c) 9 (d) 19
  2. 2.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 188 (c) 187 (d) 178
  3. 3.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
  4. 4.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 595 (c) 468 (d) 594
  5. 5.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) 99 (b) 11 (c) 36 (d) 33
  6. 6.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  7. 7.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 489 (c) 480 (d) 398
  8. 8.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 24 (c) 33 (d) 34
  9. 9.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 139 (c) 140 (d) 130
  10. 10.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 567 (c) 450 (d) 568
  11. 11.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
  12. 12.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 349 (b) 348 (c) 339 (d) 304
  13. 13.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) 45 (b) 48 (c) 15 (d) 135
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 16 (b) 5 (c) 15 (d) 17
  15. 15.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 12 (c) 108 (d) 39
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 6 (b) 4 (c) 7 (d) 5
  17. 17.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 95 (c) 86 (d) 104
  18. 18.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) 216 (c) 72 (d) 75
  19. 19.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) 18 (d) 21
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 15 (b) 4 (c) 13 (d) 14
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 57? (a) 3 (b) 4 (c) 6 (d) 5
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 14 (b) 16 (c) 4 (d) 15
  23. 23.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 384 (c) 334 (d) 393
  24. 24.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  25. 25.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 171 (b) 162 (c) 180 (d) 172
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 18 (b) 20 (c) 8 (d) 19
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 9 (b) 21 (c) 20 (d) 19
  28. 28.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 16 (b) 18 (c) 6 (d) 17
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 13 (b) 10 (c) 12 (d) 9
  31. 31.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 123 (b) 124 (c) 114 (d) 132
  32. 32.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
  33. 33.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 79? (a) 7 (b) 9 (c) 8 (d) 6
  35. 35.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) 16 (c) 144 (d) 51
  36. 36.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) 516 (c) 422 (d) 525
  37. 37.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 7 (d) 5
  38. 38.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 78 (c) 86 (d) 77
  39. 39.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  40. 40.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 336 (c) 346 (d) 302

Answer key

  1. 20
  2. 187
  3. 66
  4. 594
  5. 33
  6. 5
  7. 489
  8. 33
  9. 139
  10. 567
  11. 9
  12. 348
  13. 45
  14. 16
  15. 36
  16. 6
  17. 95
  18. 72
  19. 18
  20. 14
  21. 5
  22. 15
  23. 393
  24. 5
  25. 171
  26. 19
  27. 20
  28. 8
  29. 17
  30. 12
  31. 123
  32. 7
  33. 2
  34. 8
  35. 48
  36. 525
  37. 6
  38. 77
  39. 6
  40. 345

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