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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 604 · 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.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 143 (b) 144 (c) 134 (d) 152
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 19 (b) 20 (c) 8 (d) 18
  3. 3.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 30 (c) 39 (d) 40
  4. 4.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  5. 5.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 278 (c) 309 (d) 310
  6. 6.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
  7. 7.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) 60 (c) 171 (d) 19
  8. 8.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 178 (c) 168 (d) 177
  9. 9.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) 72 (d) 69
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 15 (b) 3 (c) 14 (d) 13
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 66? (a) 6 (b) 5 (c) 4 (d) 7
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 64? (a) 7 (b) 4 (c) 5 (d) 6
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 4 (b) 2 (c) 3 (d) 1
  14. 14.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  15. 15.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
  16. 16.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 309 (b) 319 (c) 284 (d) 318
  17. 17.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  18. 18.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 332 (c) 391 (d) 381
  19. 19.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 286 (c) 262 (d) 276
  20. 20.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 17 (d) 4
  21. 21.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 181 (c) 172 (d) 190
  22. 22.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 14 (b) 16 (c) 15 (d) 4
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 2 (b) 4 (c) 3 (d) 5
  25. 25.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 523 (b) 522 (c) 420 (d) 513
  26. 26.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 504 (c) 514 (d) 513
  27. 27.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 8 (d) 10
  28. 28.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 564 (b) 555 (c) 565 (d) 448
  29. 29.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 357 (c) 358 (d) 310
  30. 30.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) 14 (d) 126
  31. 31.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  32. 32.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 18 (b) 20 (c) 19 (d) 8
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 4 (b) 14 (c) 15 (d) 16
  35. 35.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 316 (c) 366 (d) 367
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 19 (b) 20 (c) 9 (d) 21
  37. 37.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 6 (b) 9 (c) 8 (d) 4
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 83? (a) 8 (b) 20 (c) 18 (d) 19
  40. 40.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6

Answer key

  1. 143
  2. 19
  3. 39
  4. 5
  5. 309
  6. 18
  7. 57
  8. 177
  9. 69
  10. 14
  11. 6
  12. 6
  13. 3
  14. 6
  15. 30
  16. 318
  17. 7
  18. 390
  19. 285
  20. 3
  21. 181
  22. 3
  23. 15
  24. 4
  25. 522
  26. 513
  27. 9
  28. 564
  29. 357
  30. 42
  31. 4
  32. 9
  33. 19
  34. 15
  35. 366
  36. 20
  37. 6
  38. 8
  39. 19
  40. 5

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