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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 675 · 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 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 405 (c) 406 (d) 396
  2. 2.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 243 (c) 253 (d) 252
  3. 3.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 21 (c) 7 (d) 24
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 68? (a) 17 (b) 15 (c) 16 (d) 6
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 4 (b) 3 (c) 2 (d) 5
  7. 7.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 609 (c) 478 (d) 600
  8. 8.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) 60 (b) 180 (c) 20 (d) 63
  9. 9.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
  10. 10.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) 30 (b) 9 (c) 81 (d) 27
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 10 (b) 9 (c) 7 (d) 6
  12. 12.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 129 (c) 138 (d) 130
  13. 13.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) 72 (c) 23 (d) 207
  14. 14.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  15. 15.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 90? (a) 9 (b) 18 (c) 19 (d) 20
  17. 17.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 471 (b) 472 (c) 462 (d) 386
  18. 18.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
  19. 19.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  20. 20.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 5 (b) 15 (c) 17 (d) 16
  22. 22.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 478 (b) 468 (c) 477 (d) 390
  23. 23.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 321 (c) 322 (d) 312
  24. 24.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 211 (b) 201 (c) 210 (d) 212
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 92? (a) 19 (b) 9 (c) 20 (d) 18
  26. 26.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 603 (c) 604 (d) 594
  27. 27.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  28. 28.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) 162 (c) 18 (d) 57
  29. 29.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 267 (c) 277 (d) 276
  30. 30.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) 5 (b) 18 (c) 15 (d) 45
  31. 31.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 4 (d) 2
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 9 (b) 20 (c) 18 (d) 19
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 88? (a) 18 (b) 8 (c) 19 (d) 20
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 40? (a) 2 (b) 3 (c) 5 (d) 4
  35. 35.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  36. 36.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) 33 (b) 30 (c) 90 (d) 10
  37. 37.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) 24 (b) 72 (c) 8 (d) 27
  38. 38.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 169 (b) 170 (c) 178 (d) 160
  39. 39.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 132 (c) 124 (d) 123
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 75? (a) 5 (b) 6 (c) 8 (d) 7

Answer key

  1. 405
  2. 252
  3. 21
  4. 5
  5. 16
  6. 4
  7. 609
  8. 60
  9. 71
  10. 27
  11. 9
  12. 129
  13. 69
  14. 7
  15. 4
  16. 19
  17. 471
  18. 2
  19. 3
  20. 8
  21. 16
  22. 477
  23. 321
  24. 210
  25. 19
  26. 603
  27. 4
  28. 54
  29. 276
  30. 15
  31. 3
  32. 19
  33. 19
  34. 4
  35. 6
  36. 30
  37. 24
  38. 169
  39. 123
  40. 7

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