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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 235 · 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 4 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 20 (d) 19
  2. 2.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 235 (b) 228 (c) 225 (d) 234
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 17 (b) 6 (c) 18 (d) 16
  4. 4.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  5. 5.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 290 (b) 328 (c) 318 (d) 327
  6. 6.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) 21 (d) 18
  7. 7.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 98 (c) 80 (d) 89
  8. 8.The numbers 3 to 11 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) 24 (c) 21 (d) 7
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 18 (b) 19 (c) 17 (d) 8
  10. 10.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 222 (c) 232 (d) 231
  11. 11.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 603 (c) 613 (d) 612
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 60? (a) 7 (b) 8 (c) 6 (d) 5
  13. 13.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) 126 (b) 42 (c) 45 (d) 14
  14. 14.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 603 (c) 604 (d) 594
  15. 15.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 523 (c) 522 (d) 513
  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) 54 (b) 57 (c) 162 (d) 18
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 62? (a) 4 (b) 6 (c) 7 (d) 5
  18. 18.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) 9 (c) 30 (d) 27
  19. 19.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 8 (d) 10
  20. 20.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 214 (b) 321 (c) 204 (d) 213
  21. 21.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  22. 22.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 88 (c) 80 (d) 79
  23. 23.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
  24. 24.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) 66 (b) 21 (c) 189 (d) 63
  25. 25.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 53 (b) 62 (c) 54 (d) 44
  26. 26.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 271 (b) 252 (c) 261 (d) 270
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 70? (a) 7 (b) 6 (c) 8 (d) 9
  28. 28.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) 180 (b) 63 (c) 60 (d) 20
  29. 29.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 426 (c) 362 (d) 435
  30. 30.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) 135 (b) 48 (c) 15 (d) 45
  31. 31.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  32. 32.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 550 (b) 540 (c) 549 (d) 438
  33. 33.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 38? (a) 4 (b) 3 (c) 5 (d) 2
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 88? (a) 18 (b) 8 (c) 19 (d) 20
  36. 36.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 265 (c) 248 (d) 255
  37. 37.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 434 (b) 544 (c) 534 (d) 543
  38. 38.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 324 (c) 325 (d) 315
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 68? (a) 7 (b) 6 (c) 5 (d) 8
  40. 40.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 162 (c) 152 (d) 161

Answer key

  1. 19
  2. 234
  3. 17
  4. 4
  5. 327
  6. 18
  7. 89
  8. 21
  9. 18
  10. 231
  11. 612
  12. 7
  13. 42
  14. 603
  15. 522
  16. 54
  17. 6
  18. 27
  19. 7
  20. 213
  21. 5
  22. 79
  23. 8
  24. 63
  25. 53
  26. 270
  27. 8
  28. 60
  29. 435
  30. 45
  31. 3
  32. 549
  33. 7
  34. 4
  35. 19
  36. 264
  37. 543
  38. 324
  39. 7
  40. 161

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