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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 84 · 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 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 336 (c) 346 (d) 302
  2. 2.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) 36 (b) 12 (c) 108 (d) 39
  3. 3.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 470 (b) 597 (c) 588 (d) 598
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 3 (b) 4 (c) 2 (d) 5
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
  6. 6.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 432 (c) 423 (d) 433
  7. 7.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 544 (c) 434 (d) 543
  8. 8.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 17 (b) 8 (c) 18 (d) 19
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 3 (b) 4 (c) 2 (d) 5
  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) 54 (b) 18 (c) 57 (d) 162
  12. 12.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
  13. 13.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 5 (d) 3
  14. 14.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) 16 (d) 48
  15. 15.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 110 (c) 109 (d) 118
  16. 16.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 274 (c) 294 (d) 303
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 18 (b) 17 (c) 6 (d) 16
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 4 (b) 1 (c) 2 (d) 3
  19. 19.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 53 (c) 44 (d) 54
  20. 20.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) 6 (b) 54 (c) 21 (d) 18
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 4 (b) 5 (c) 6 (d) 7
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 2 (b) 5 (c) 3 (d) 4
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 20 (b) 21 (c) 19 (d) 9
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 55? (a) 5 (b) 15 (c) 16 (d) 17
  25. 25.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  26. 26.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 523 (c) 420 (d) 522
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 2 (b) 1 (c) 4 (d) 3
  28. 28.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) 75 (c) 72 (d) 24
  29. 29.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  30. 30.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 9 (d) 11
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 6 (b) 4 (c) 3 (d) 5
  32. 32.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 188 (c) 180 (d) 179
  33. 33.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 4 (b) 2 (c) 3 (d) 5
  35. 35.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) 8 (b) 27 (c) 72 (d) 24
  36. 36.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 298 (c) 297 (d) 270
  37. 37.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 145 (c) 146 (d) 154
  38. 38.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 266 (b) 292 (c) 282 (d) 291
  39. 39.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 90 (c) 98 (d) 89
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 18 (b) 17 (c) 19 (d) 8

Answer key

  1. 345
  2. 36
  3. 597
  4. 4
  5. 6
  6. 432
  7. 543
  8. 6
  9. 18
  10. 4
  11. 54
  12. 216
  13. 4
  14. 48
  15. 109
  16. 303
  17. 17
  18. 3
  19. 53
  20. 18
  21. 6
  22. 4
  23. 20
  24. 16
  25. 3
  26. 522
  27. 3
  28. 72
  29. 7
  30. 9
  31. 5
  32. 179
  33. 5
  34. 4
  35. 24
  36. 297
  37. 145
  38. 291
  39. 89
  40. 18

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