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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 369 · 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 6 written when you write all the numbers from 1 to 54? (a) 5 (b) 4 (c) 3 (d) 6
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 16 (b) 18 (c) 6 (d) 17
  3. 3.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 338 (b) 399 (c) 400 (d) 390
  4. 4.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 501 (b) 511 (c) 412 (d) 510
  5. 5.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 33 (c) 42 (d) 24
  6. 6.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 161 (c) 170 (d) 152
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 14 (b) 15 (c) 16 (d) 4
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 6 (b) 16 (c) 15 (d) 17
  9. 9.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 8 (d) 7
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 9 (b) 19 (c) 20 (d) 21
  12. 12.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) 16 (c) 51 (d) 48
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 18 (b) 20 (c) 19 (d) 9
  14. 14.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 330 (c) 298 (d) 340
  15. 15.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4
  16. 16.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 568 (b) 450 (c) 567 (d) 558
  17. 17.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 17 (b) 18 (c) 7 (d) 19
  19. 19.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 261 (c) 271 (d) 252
  20. 20.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  21. 21.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 532 (c) 426 (d) 522
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 20 (b) 19 (c) 18 (d) 8
  23. 23.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 270 (c) 288 (d) 298
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 17 (b) 18 (c) 7 (d) 19
  25. 25.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  26. 26.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) 162 (b) 54 (c) 57 (d) 18
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 68? (a) 15 (b) 17 (c) 6 (d) 16
  28. 28.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 88 (c) 97 (d) 106
  29. 29.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) 291 (c) 282 (d) 292
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 50? (a) 7 (b) 5 (c) 6 (d) 4
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 6 (b) 10 (c) 7 (d) 9
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 5 (b) 3 (c) 4 (d) 2
  33. 33.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 249 (c) 240 (d) 238
  34. 34.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 619 (c) 484 (d) 609
  35. 35.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 404 (c) 499 (d) 498
  36. 36.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 336 (c) 387 (d) 397
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 18 (b) 16 (c) 6 (d) 17
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 7 (b) 4 (c) 5 (d) 6
  39. 39.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 11 (b) 33 (c) 36 (d) 99
  40. 40.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) 434 (c) 544 (d) 543

Answer key

  1. 5
  2. 17
  3. 399
  4. 510
  5. 33
  6. 161
  7. 15
  8. 16
  9. 9
  10. 7
  11. 20
  12. 48
  13. 19
  14. 339
  15. 5
  16. 567
  17. 4
  18. 18
  19. 270
  20. 3
  21. 531
  22. 19
  23. 297
  24. 18
  25. 2
  26. 54
  27. 16
  28. 97
  29. 291
  30. 6
  31. 9
  32. 4
  33. 249
  34. 618
  35. 498
  36. 396
  37. 17
  38. 6
  39. 33
  40. 543

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