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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 596 · 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 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 204 (c) 198 (d) 199
  2. 2.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) 60 (b) 63 (c) 180 (d) 20
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 9 (b) 21 (c) 20 (d) 19
  4. 4.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 153 (b) 17 (c) 54 (d) 51
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 19 (b) 18 (c) 8 (d) 20
  6. 6.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) 23 (c) 207 (d) 69
  7. 7.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 98 (c) 108 (d) 107
  8. 8.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) 108 (c) 12 (d) 36
  9. 9.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 12 (b) 10 (c) 8 (d) 13
  11. 11.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 10 (c) 30 (d) 90
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 13 (b) 10 (c) 12 (d) 7
  13. 13.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  14. 14.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 62 (c) 61 (d) 52
  15. 15.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) 16 (b) 144 (c) 51 (d) 48
  16. 16.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 411 (c) 412 (d) 346
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 7 (b) 5 (c) 6 (d) 8
  18. 18.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 18 (b) 17 (c) 7 (d) 19
  20. 20.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 556 (b) 442 (c) 546 (d) 555
  21. 21.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 640 (b) 498 (c) 639 (d) 630
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 1 (d) 3
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 15 (b) 14 (c) 16 (d) 4
  24. 24.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 337 (b) 296 (c) 336 (d) 327
  25. 25.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 80 (c) 90 (d) 89
  26. 26.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) 21 (b) 18 (c) 6 (d) 54
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 69? (a) 16 (b) 18 (c) 17 (d) 6
  28. 28.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 66 (c) 75 (d) 84
  29. 29.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  30. 30.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 319 (b) 309 (c) 284 (d) 318
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 8 (b) 19 (c) 18 (d) 20
  32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 1 (b) 2 (c) 3 (d) 4
  33. 33.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 77 (c) 78 (d) 68
  34. 34.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) 228 (c) 238 (d) 230
  35. 35.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) 63 (b) 21 (c) 189 (d) 66
  36. 36.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) 15 (c) 135 (d) 48
  37. 37.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 63 (b) 64 (c) 72 (d) 54
  38. 38.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 490 (c) 398 (d) 489
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 7 (b) 4 (c) 6 (d) 5
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 93? (a) 18 (b) 9 (c) 20 (d) 19

Answer key

  1. 198
  2. 60
  3. 20
  4. 51
  5. 19
  6. 69
  7. 107
  8. 36
  9. 7
  10. 12
  11. 30
  12. 12
  13. 5
  14. 61
  15. 48
  16. 411
  17. 7
  18. 4
  19. 18
  20. 555
  21. 639
  22. 3
  23. 15
  24. 336
  25. 89
  26. 18
  27. 17
  28. 75
  29. 6
  30. 318
  31. 19
  32. 3
  33. 77
  34. 237
  35. 63
  36. 45
  37. 63
  38. 489
  39. 6
  40. 19

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