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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 944 · 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 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 337 (b) 327 (c) 296 (d) 336
  2. 2.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 519 (c) 510 (d) 520
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 5 (b) 3 (c) 4 (d) 2
  5. 5.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 164 (c) 172 (d) 163
  6. 6.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 414 (c) 415 (d) 405
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 16 (b) 18 (c) 6 (d) 17
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 8 (d) 18
  9. 9.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
  10. 10.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  11. 11.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 238 (c) 250 (d) 249
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 99? (a) 20 (b) 9 (c) 21 (d) 19
  14. 14.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) 22 (b) 198 (c) 66 (d) 69
  15. 15.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  16. 16.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 379 (c) 378 (d) 324
  17. 17.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 7 (d) 12
  18. 18.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
  19. 19.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 205 (c) 208 (d) 204
  20. 20.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) 78 (c) 77 (d) 68
  21. 21.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  22. 22.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 242 (c) 256 (d) 246
  23. 23.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 189 (c) 190 (d) 180
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 6 (b) 7 (c) 8 (d) 9
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 4 (b) 5 (c) 6 (d) 3
  26. 26.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 234 (c) 351 (d) 243
  27. 27.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 478 (c) 610 (d) 600
  28. 28.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 549 (c) 550 (d) 540
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 4 (b) 16 (c) 14 (d) 15
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 21 (d) 19
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 4 (b) 6 (c) 3 (d) 5
  32. 32.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 621 (c) 612 (d) 622
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 1 (b) 2 (c) 4 (d) 3
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 86? (a) 20 (b) 19 (c) 8 (d) 18
  35. 35.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 349 (b) 339 (c) 304 (d) 348
  36. 36.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) 104 (c) 94 (d) 112
  37. 37.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 11 (b) 3 (c) 10 (d) 12
  39. 39.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
  40. 40.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10

Answer key

  1. 336
  2. 519
  3. 5
  4. 4
  5. 163
  6. 414
  7. 17
  8. 18
  9. 2
  10. 6
  11. 249
  12. 9
  13. 20
  14. 66
  15. 6
  16. 378
  17. 8
  18. 36
  19. 204
  20. 77
  21. 5
  22. 255
  23. 189
  24. 8
  25. 5
  26. 243
  27. 609
  28. 549
  29. 15
  30. 20
  31. 5
  32. 621
  33. 3
  34. 19
  35. 348
  36. 103
  37. 4
  38. 11
  39. 7
  40. 3

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