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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 345 · 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 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 390 (c) 468 (d) 478
  2. 2.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 616 (b) 615 (c) 482 (d) 606
  3. 3.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 630 (c) 639 (d) 640
  4. 4.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 171 (c) 60 (d) 57
  5. 5.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 6 (d) 5
  6. 6.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) 39 (b) 13 (c) 117 (d) 42
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 84? (a) 8 (b) 18 (c) 17 (d) 19
  8. 8.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 46 (c) 28 (d) 37
  9. 9.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 189 (b) 21 (c) 66 (d) 63
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 4 (b) 1 (c) 2 (d) 3
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 4 (b) 5 (c) 3 (d) 2
  13. 13.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) 235 (c) 225 (d) 234
  14. 14.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 121 (b) 130 (c) 112 (d) 122
  15. 15.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 256 (c) 277 (d) 267
  16. 16.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 2 (b) 3 (c) 5 (d) 4
  18. 18.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 223 (c) 213 (d) 222
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 50? (a) 7 (b) 5 (c) 4 (d) 6
  20. 20.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 562 (b) 446 (c) 561 (d) 552
  21. 21.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 14 (b) 3 (c) 13 (d) 15
  23. 23.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) 62 (c) 52 (d) 70
  24. 24.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  25. 25.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 307 (b) 306 (c) 276 (d) 297
  26. 26.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 217 (b) 207 (c) 324 (d) 216
  27. 27.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) 51 (b) 144 (c) 48 (d) 16
  28. 28.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 4 (b) 14 (c) 15 (d) 16
  30. 30.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) 42 (b) 45 (c) 14 (d) 126
  31. 31.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 457 (b) 456 (c) 447 (d) 376
  32. 32.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
  33. 33.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 574 (b) 573 (c) 564 (d) 454
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 3 (b) 2 (c) 4 (d) 5
  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) 11 (b) 33 (c) 36 (d) 99
  36. 36.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 633 (c) 634 (d) 494
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 93? (a) 20 (b) 18 (c) 9 (d) 19
  38. 38.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 24 (c) 72 (d) 8
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 6 (b) 5 (c) 8 (d) 7
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 8 (b) 19 (c) 17 (d) 18

Answer key

  1. 477
  2. 615
  3. 639
  4. 57
  5. 6
  6. 39
  7. 18
  8. 37
  9. 63
  10. 3
  11. 3
  12. 4
  13. 234
  14. 121
  15. 276
  16. 9
  17. 4
  18. 222
  19. 6
  20. 561
  21. 9
  22. 14
  23. 61
  24. 8
  25. 306
  26. 216
  27. 48
  28. 7
  29. 15
  30. 42
  31. 456
  32. 69
  33. 573
  34. 4
  35. 33
  36. 633
  37. 19
  38. 24
  39. 7
  40. 18

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