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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 554 · 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 two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  2. 2.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 272 (b) 301 (c) 300 (d) 291
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 17 (b) 19 (c) 18 (d) 8
  4. 4.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 352 (c) 342 (d) 351
  5. 5.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 119 (b) 110 (c) 120 (d) 128
  6. 6.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 307 (b) 297 (c) 276 (d) 306
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 4 (b) 2 (c) 1 (d) 3
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 19 (b) 17 (c) 18 (d) 7
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 6 (b) 4 (c) 3 (d) 5
  10. 10.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 120 (c) 138 (d) 129
  11. 11.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 316 (c) 315 (d) 282
  12. 12.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 117 (c) 126 (d) 118
  13. 13.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 80 (c) 71 (d) 62
  14. 14.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 325 (b) 315 (c) 288 (d) 324
  15. 15.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 9 (b) 20 (c) 21 (d) 19
  17. 17.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) 108 (b) 12 (c) 39 (d) 36
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 15 (b) 4 (c) 14 (d) 16
  19. 19.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  20. 20.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) 72 (c) 24 (d) 27
  21. 21.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 131 (c) 122 (d) 132
  22. 22.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 5 (d) 16
  23. 23.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 91 (c) 100 (d) 82
  24. 24.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 7 (b) 16 (c) 18 (d) 17
  26. 26.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  27. 27.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) 18 (b) 21 (c) 6 (d) 54
  28. 28.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  29. 29.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 20 (c) 63 (d) 60
  30. 30.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 288 (c) 279 (d) 289
  31. 31.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) 418 (c) 519 (d) 520
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 16 (b) 15 (c) 17 (d) 6
  33. 33.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 48 (c) 45 (d) 15
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 18 (b) 16 (c) 6 (d) 17
  35. 35.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 19 (b) 18 (c) 8 (d) 17
  37. 37.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) 198 (b) 69 (c) 22 (d) 66
  38. 38.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
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 50? (a) 4 (b) 6 (c) 3 (d) 5
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 54? (a) 4 (b) 5 (c) 6 (d) 3

Answer key

  1. 2
  2. 300
  3. 18
  4. 351
  5. 119
  6. 306
  7. 3
  8. 18
  9. 5
  10. 129
  11. 315
  12. 117
  13. 71
  14. 324
  15. 8
  16. 20
  17. 36
  18. 15
  19. 2
  20. 24
  21. 131
  22. 4
  23. 91
  24. 3
  25. 17
  26. 9
  27. 18
  28. 3
  29. 60
  30. 288
  31. 519
  32. 16
  33. 45
  34. 17
  35. 4
  36. 18
  37. 66
  38. 54
  39. 5
  40. 5

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