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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 29 · 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 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 462 (c) 586 (d) 576
  2. 2.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) 117 (c) 42 (d) 13
  3. 3.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
  4. 4.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) 39 (b) 12 (c) 36 (d) 108
  5. 5.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  6. 6.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 2 (d) 4
  7. 7.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 8 (d) 9
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 9 (b) 18 (c) 19 (d) 20
  9. 9.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 360 (c) 433 (d) 423
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 4 (b) 2 (c) 5 (d) 3
  11. 11.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) 54 (c) 18 (d) 57
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 67? (a) 15 (b) 14 (c) 16 (d) 6
  13. 13.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) 9 (b) 27 (c) 30 (d) 81
  14. 14.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 316 (c) 306 (d) 315
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 15 (b) 5 (c) 16 (d) 14
  16. 16.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  17. 17.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 180 (c) 60 (d) 20
  18. 18.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  19. 19.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 178 (c) 177 (d) 168
  20. 20.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 4 (d) 3
  21. 21.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 350 (b) 408 (c) 418 (d) 417
  22. 22.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 146 (c) 136 (d) 145
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 6 (b) 5 (c) 3 (d) 4
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 2 (b) 1 (c) 3 (d) 4
  25. 25.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 26 (c) 44 (d) 35
  26. 26.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 288 (c) 324 (d) 325
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 74? (a) 7 (b) 8 (c) 5 (d) 6
  28. 28.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) 69 (c) 207 (d) 23
  29. 29.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 236 (b) 237 (c) 247 (d) 246
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 18 (b) 16 (c) 6 (d) 17
  31. 31.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 292 (c) 291 (d) 266
  32. 32.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 103 (b) 112 (c) 104 (d) 94
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 61? (a) 5 (b) 6 (c) 4 (d) 7
  34. 34.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) 75 (b) 24 (c) 72 (d) 216
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 14 (b) 15 (c) 13 (d) 3
  36. 36.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) 334 (c) 384 (d) 393
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 3 (b) 2 (c) 5 (d) 4
  38. 38.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) 249 (c) 238 (d) 240
  39. 39.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 87 (c) 78 (d) 96
  40. 40.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 525 (c) 526 (d) 422

Answer key

  1. 585
  2. 39
  3. 8
  4. 36
  5. 7
  6. 3
  7. 8
  8. 19
  9. 432
  10. 4
  11. 54
  12. 15
  13. 27
  14. 315
  15. 15
  16. 2
  17. 60
  18. 6
  19. 177
  20. 4
  21. 417
  22. 145
  23. 5
  24. 3
  25. 35
  26. 324
  27. 7
  28. 69
  29. 246
  30. 17
  31. 291
  32. 103
  33. 6
  34. 72
  35. 14
  36. 393
  37. 4
  38. 249
  39. 87
  40. 525

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