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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 545 · 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 7 written when you write all the numbers from 1 to 94? (a) 18 (b) 19 (c) 20 (d) 9
  2. 2.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 351 (c) 352 (d) 306
  3. 3.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  4. 4.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 460 (c) 459 (d) 378
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 18 (b) 16 (c) 6 (d) 17
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 5 (b) 3 (c) 4 (d) 2
  7. 7.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  8. 8.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 9 (d) 11
  9. 9.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 538 (c) 528 (d) 537
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 4 (b) 15 (c) 16 (d) 14
  11. 11.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 260 (b) 273 (c) 282 (d) 283
  12. 12.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  13. 13.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 17 (b) 18 (c) 7 (d) 19
  15. 15.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) 207 (c) 69 (d) 72
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 4 (b) 2 (c) 3 (d) 5
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 15 (b) 4 (c) 14 (d) 16
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 5 (b) 6 (c) 3 (d) 4
  19. 19.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) 6 (c) 18 (d) 54
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 4 (b) 3 (c) 2 (d) 5
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 4 (b) 2 (c) 3 (d) 1
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 4 (b) 2 (c) 1 (d) 3
  23. 23.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 360 (c) 361 (d) 351
  24. 24.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 22 (c) 40 (d) 31
  25. 25.The numbers 9 to 17 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) 13 (c) 42 (d) 117
  26. 26.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
  27. 27.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 502 (c) 501 (d) 406
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 4 (b) 10 (c) 11 (d) 9
  29. 29.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 79 (c) 88 (d) 80
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 16 (b) 6 (c) 18 (d) 17
  31. 31.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 432 (c) 433 (d) 360
  32. 32.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  33. 33.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 207 (c) 198 (d) 210
  34. 34.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 500 (b) 633 (c) 643 (d) 642
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 7 (d) 18
  36. 36.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 14 (b) 15 (c) 4 (d) 16
  38. 38.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 600 (c) 601 (d) 591
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 83? (a) 19 (b) 20 (c) 8 (d) 18
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 6 (b) 16 (c) 15 (d) 17

Answer key

  1. 19
  2. 351
  3. 7
  4. 459
  5. 17
  6. 4
  7. 9
  8. 9
  9. 537
  10. 15
  11. 282
  12. 2
  13. 4
  14. 18
  15. 69
  16. 4
  17. 15
  18. 5
  19. 18
  20. 4
  21. 3
  22. 3
  23. 360
  24. 31
  25. 39
  26. 636
  27. 501
  28. 10
  29. 79
  30. 17
  31. 432
  32. 3
  33. 207
  34. 642
  35. 18
  36. 3
  37. 15
  38. 600
  39. 19
  40. 16

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