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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 712 · 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) 1 (c) 3 (d) 2
  2. 2.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 83 (c) 84 (d) 74
  3. 3.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  4. 4.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 9 (d) 11
  5. 5.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 126 (c) 136 (d) 135
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 2 (b) 4 (c) 5 (d) 3
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 18 (b) 9 (c) 20 (d) 19
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 4 (b) 5 (c) 7 (d) 6
  9. 9.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) 19 (b) 60 (c) 57 (d) 171
  10. 10.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 279 (c) 264 (d) 289
  11. 11.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 4 (d) 17
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 97? (a) 20 (b) 19 (c) 9 (d) 21
  13. 13.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 230 (b) 237 (c) 238 (d) 228
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 9 (b) 20 (c) 19 (d) 21
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 90? (a) 20 (b) 9 (c) 18 (d) 19
  16. 16.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
  17. 17.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 619 (b) 609 (c) 484 (d) 618
  18. 18.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
  19. 19.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  20. 20.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 13 (d) 6
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 60? (a) 17 (b) 16 (c) 15 (d) 6
  22. 22.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 235 (b) 225 (c) 234 (d) 228
  23. 23.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 214 (c) 213 (d) 204
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 7 (b) 17 (c) 18 (d) 16
  25. 25.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 8 (b) 5 (c) 7 (d) 6
  27. 27.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 17 (c) 54 (d) 153
  28. 28.The numbers 1 to 9 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) 45 (c) 15 (d) 5
  29. 29.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) 354 (d) 364
  30. 30.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 324 (c) 216 (d) 217
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 15 (b) 4 (c) 14 (d) 16
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 7 (b) 18 (c) 17 (d) 16
  33. 33.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
  34. 34.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 123 (b) 132 (c) 124 (d) 114
  35. 35.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 142 (c) 151 (d) 152
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 21 (b) 20 (c) 9 (d) 19
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 3 (b) 2 (c) 1 (d) 4
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 7 (b) 18 (c) 19 (d) 17
  39. 39.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) 20 (b) 63 (c) 180 (d) 60
  40. 40.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 309 (b) 300 (c) 278 (d) 310

Answer key

  1. 2
  2. 83
  3. 4
  4. 9
  5. 135
  6. 4
  7. 19
  8. 6
  9. 57
  10. 288
  11. 3
  12. 20
  13. 237
  14. 20
  15. 19
  16. 63
  17. 618
  18. 7
  19. 3
  20. 7
  21. 16
  22. 234
  23. 213
  24. 17
  25. 8
  26. 7
  27. 51
  28. 15
  29. 363
  30. 216
  31. 15
  32. 17
  33. 5
  34. 123
  35. 151
  36. 20
  37. 3
  38. 18
  39. 60
  40. 309

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