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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 728 · 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 7? (a) 7 (b) 6 (c) 10 (d) 8
  2. 2.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 6 (d) 10
  3. 3.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) 36 (d) 44
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 5 (b) 2 (c) 3 (d) 4
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 65? (a) 6 (b) 17 (c) 18 (d) 16
  6. 6.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 213 (b) 204 (c) 214 (d) 321
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 15 (b) 14 (c) 13 (d) 3
  8. 8.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) 182 (c) 174 (d) 173
  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) 57 (b) 60 (c) 171 (d) 19
  10. 10.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) 21 (b) 63 (c) 66 (d) 189
  11. 11.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 218 (b) 219 (c) 210 (d) 220
  12. 12.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  13. 13.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
  14. 14.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) 9 (b) 27 (c) 30 (d) 81
  15. 15.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 15 (b) 13 (c) 14 (d) 4
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 18 (b) 17 (c) 6 (d) 16
  18. 18.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 272 (c) 291 (d) 300
  19. 19.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) 69 (b) 23 (c) 207 (d) 72
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 4 (b) 1 (c) 2 (d) 3
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 4 (b) 1 (c) 2 (d) 3
  22. 22.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 12 (b) 3 (c) 11 (d) 10
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 4 (b) 6 (c) 5 (d) 3
  25. 25.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 146 (c) 128 (d) 137
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 2 (b) 1 (c) 4 (d) 3
  27. 27.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 82 (c) 72 (d) 81
  28. 28.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  29. 29.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 390 (c) 391 (d) 332
  30. 30.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 54 (c) 64 (d) 63
  31. 31.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 392 (b) 471 (c) 481 (d) 480
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 88? (a) 20 (b) 8 (c) 19 (d) 18
  33. 33.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) 18 (c) 6 (d) 54
  34. 34.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) 15 (b) 45 (c) 135 (d) 48
  35. 35.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 403 (b) 402 (c) 340 (d) 393
  36. 36.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
  37. 37.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
  38. 38.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 496 (b) 636 (c) 627 (d) 637
  39. 39.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 295 (b) 294 (c) 285 (d) 268
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 84? (a) 8 (b) 18 (c) 19 (d) 20

Answer key

  1. 7
  2. 5
  3. 35
  4. 4
  5. 17
  6. 213
  7. 14
  8. 173
  9. 57
  10. 63
  11. 219
  12. 2
  13. 9
  14. 27
  15. 3
  16. 14
  17. 17
  18. 300
  19. 69
  20. 3
  21. 3
  22. 7
  23. 11
  24. 5
  25. 137
  26. 3
  27. 81
  28. 4
  29. 390
  30. 63
  31. 480
  32. 19
  33. 18
  34. 45
  35. 402
  36. 9
  37. 3
  38. 636
  39. 294
  40. 19

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