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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 262 · 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 5? (a) 6 (b) 5 (c) 4 (d) 10
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 12 (b) 6 (c) 9 (d) 11
  3. 3.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 297 (c) 298 (d) 270
  4. 4.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 26 (b) 35 (c) 44 (d) 36
  5. 5.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 384 (c) 394 (d) 334
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 4 (b) 6 (c) 7 (d) 3
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 4 (b) 15 (c) 14 (d) 16
  8. 8.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 170 (c) 179 (d) 188
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 91? (a) 18 (b) 19 (c) 20 (d) 9
  10. 10.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 165 (c) 174 (d) 156
  11. 11.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) 45 (b) 42 (c) 126 (d) 14
  12. 12.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 90 (c) 33 (d) 10
  13. 13.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 320 (b) 372 (c) 363 (d) 373
  14. 14.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 13 (b) 3 (c) 15 (d) 14
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 76? (a) 17 (b) 7 (c) 18 (d) 19
  17. 17.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 214 (b) 213 (c) 204 (d) 321
  18. 18.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) 48 (c) 16 (d) 51
  19. 19.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 140 (c) 139 (d) 148
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 7 (b) 8 (c) 4 (d) 5
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 69? (a) 6 (b) 17 (c) 18 (d) 16
  22. 22.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  23. 23.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 17 (b) 16 (c) 18 (d) 6
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 5 (b) 3 (c) 2 (d) 4
  26. 26.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  27. 27.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 12 (d) 9
  28. 28.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 327 (c) 290 (d) 318
  29. 29.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 9 (b) 19 (c) 21 (d) 20
  31. 31.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 174 (c) 173 (d) 182
  32. 32.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 410 (c) 508 (d) 498
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 16 (b) 15 (c) 14 (d) 4
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 9 (b) 20 (c) 18 (d) 19
  35. 35.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 98 (c) 107 (d) 108
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 70? (a) 7 (b) 18 (c) 17 (d) 16
  37. 37.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 228 (c) 224 (d) 229
  38. 38.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) 171 (b) 19 (c) 60 (d) 57
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 16 (b) 18 (c) 17 (d) 6
  40. 40.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 408 (c) 409 (d) 344

Answer key

  1. 5
  2. 11
  3. 297
  4. 35
  5. 393
  6. 6
  7. 15
  8. 179
  9. 19
  10. 165
  11. 42
  12. 30
  13. 372
  14. 2
  15. 14
  16. 18
  17. 213
  18. 48
  19. 139
  20. 7
  21. 17
  22. 4
  23. 7
  24. 17
  25. 4
  26. 2
  27. 8
  28. 327
  29. 9
  30. 20
  31. 173
  32. 507
  33. 15
  34. 19
  35. 107
  36. 17
  37. 228
  38. 57
  39. 17
  40. 408

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