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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 46 · 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 3 written when you write all the numbers from 1 to 31? (a) 6 (b) 4 (c) 5 (d) 3
  2. 2.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) 54 (c) 18 (d) 6
  3. 3.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  4. 4.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 71 (c) 72 (d) 62
  5. 5.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 228 (c) 235 (d) 225
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 19 (b) 7 (c) 18 (d) 17
  7. 7.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 14 (c) 126 (d) 45
  8. 8.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) 66 (b) 21 (c) 189 (d) 63
  9. 9.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) 48 (b) 16 (c) 51 (d) 144
  10. 10.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
  11. 11.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 525 (b) 534 (c) 428 (d) 535
  12. 12.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 81 (c) 9 (d) 30
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 8 (b) 14 (c) 11 (d) 13
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 81? (a) 8 (b) 19 (c) 18 (d) 17
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 9 (b) 19 (c) 20 (d) 21
  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) 558 (b) 567 (c) 450 (d) 568
  17. 17.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 314 (b) 363 (c) 364 (d) 354
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 4 (b) 14 (c) 15 (d) 13
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 20 (b) 9 (c) 19 (d) 21
  20. 20.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 2 (d) 17
  21. 21.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 520 (c) 418 (d) 519
  22. 22.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 153 (c) 154 (d) 144
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 6 (b) 5 (c) 7 (d) 4
  24. 24.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 113 (b) 122 (c) 114 (d) 104
  25. 25.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 356 (b) 417 (c) 427 (d) 426
  26. 26.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) 99 (b) 33 (c) 36 (d) 11
  27. 27.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 7 (b) 4 (c) 6 (d) 5
  29. 29.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 149 (b) 140 (c) 150 (d) 158
  30. 30.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 550 (b) 438 (c) 540 (d) 549
  31. 31.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 528 (b) 424 (c) 529 (d) 519
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 20 (b) 21 (c) 19 (d) 9
  33. 33.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 73 (c) 64 (d) 82
  34. 34.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 193 (b) 200 (c) 183 (d) 192
  35. 35.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 64 (c) 55 (d) 46
  36. 36.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 92 (c) 91 (d) 100
  37. 37.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 19 (c) 60 (d) 171
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 3 (b) 2 (c) 4 (d) 1
  39. 39.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) 69 (b) 66 (c) 22 (d) 198
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 5 (b) 4 (c) 6 (d) 3

Answer key

  1. 5
  2. 18
  3. 6
  4. 71
  5. 234
  6. 18
  7. 42
  8. 63
  9. 48
  10. 2
  11. 534
  12. 27
  13. 13
  14. 18
  15. 20
  16. 567
  17. 363
  18. 14
  19. 20
  20. 3
  21. 519
  22. 153
  23. 6
  24. 113
  25. 426
  26. 33
  27. 8
  28. 6
  29. 149
  30. 549
  31. 528
  32. 20
  33. 73
  34. 192
  35. 55
  36. 91
  37. 57
  38. 3
  39. 66
  40. 5

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