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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 855 · 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 two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
  2. 2.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 230 (c) 228 (d) 238
  3. 3.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 155 (c) 164 (d) 146
  4. 4.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 295 (b) 294 (c) 285 (d) 268
  5. 5.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  6. 6.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) 22 (d) 69
  7. 7.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) 18 (b) 6 (c) 21 (d) 54
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 69? (a) 6 (b) 18 (c) 16 (d) 17
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 19 (b) 21 (c) 9 (d) 20
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 20 (b) 21 (c) 9 (d) 19
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 4 (b) 3 (c) 2 (d) 5
  12. 12.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  13. 13.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 152 (c) 142 (d) 151
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 11 (b) 10 (c) 12 (d) 4
  15. 15.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 525 (b) 428 (c) 535 (d) 534
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 6 (b) 18 (c) 16 (d) 17
  17. 17.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  18. 18.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 14 (b) 4 (c) 16 (d) 15
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 6 (b) 5 (c) 3 (d) 4
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 20 (b) 19 (c) 8 (d) 18
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 10 (b) 7 (c) 9 (d) 5
  23. 23.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) 144 (b) 51 (c) 48 (d) 16
  24. 24.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 453 (b) 454 (c) 374 (d) 444
  25. 25.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 555 (b) 565 (c) 448 (d) 564
  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) 45 (d) 15
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 15 (b) 4 (c) 16 (d) 14
  28. 28.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 15 (b) 16 (c) 4 (d) 14
  30. 30.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  31. 31.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) 52 (c) 62 (d) 70
  32. 32.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) 216 (b) 24 (c) 75 (d) 72
  33. 33.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) 23 (b) 69 (c) 207 (d) 72
  34. 34.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) 36 (c) 12 (d) 108
  35. 35.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  36. 36.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  37. 37.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 637 (c) 496 (d) 636
  38. 38.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 35 (b) 36 (c) 26 (d) 44
  39. 39.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 478 (c) 390 (d) 477
  40. 40.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 420 (c) 430 (d) 429

Answer key

  1. 5
  2. 237
  3. 155
  4. 294
  5. 7
  6. 66
  7. 18
  8. 17
  9. 20
  10. 20
  11. 4
  12. 4
  13. 151
  14. 11
  15. 534
  16. 17
  17. 5
  18. 9
  19. 15
  20. 5
  21. 19
  22. 9
  23. 48
  24. 453
  25. 564
  26. 15
  27. 15
  28. 3
  29. 15
  30. 7
  31. 61
  32. 72
  33. 69
  34. 36
  35. 9
  36. 8
  37. 636
  38. 35
  39. 477
  40. 429

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