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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 270 · 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 16? (a) 3 (b) 4 (c) 17 (d) 2
  2. 2.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 423 (c) 414 (d) 354
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 19 (d) 20
  4. 4.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 8 (d) 9
  5. 5.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
  6. 6.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 33 (c) 11 (d) 36
  7. 7.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) 54 (b) 51 (c) 153 (d) 17
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 43? (a) 5 (b) 4 (c) 2 (d) 3
  9. 9.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 74 (c) 66 (d) 65
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 74? (a) 18 (b) 7 (c) 16 (d) 17
  11. 11.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
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 2 (b) 3 (c) 4 (d) 5
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 20 (b) 19 (c) 9 (d) 21
  14. 14.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  15. 15.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) 54 (b) 6 (c) 18 (d) 21
  16. 16.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) 135 (d) 136
  17. 17.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 5 (d) 3
  18. 18.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 139 (c) 130 (d) 140
  19. 19.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) 367 (c) 316 (d) 366
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 20 (b) 9 (c) 19 (d) 18
  21. 21.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 6 (d) 13
  22. 22.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 630 (c) 492 (d) 631
  23. 23.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 259 (c) 258 (d) 244
  24. 24.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 324 (c) 333 (d) 294
  25. 25.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 117 (c) 42 (d) 39
  26. 26.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) 10 (b) 30 (c) 33 (d) 90
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 14 (b) 15 (c) 4 (d) 16
  28. 28.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  29. 29.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 3 (d) 2
  30. 30.The numbers 18 to 26 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) 69 (c) 198 (d) 22
  31. 31.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) 27 (c) 81 (d) 9
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 4 (d) 1
  33. 33.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 585 (c) 595 (d) 468
  34. 34.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 16 (b) 17 (c) 18 (d) 6
  36. 36.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
  37. 37.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 576 (c) 586 (d) 585
  38. 38.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 348 (c) 414 (d) 415
  39. 39.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 8 (d) 11
  40. 40.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 474 (c) 604 (d) 603

Answer key

  1. 3
  2. 423
  3. 20
  4. 8
  5. 5
  6. 33
  7. 51
  8. 4
  9. 65
  10. 17
  11. 57
  12. 4
  13. 20
  14. 2
  15. 18
  16. 135
  17. 4
  18. 139
  19. 366
  20. 19
  21. 7
  22. 630
  23. 258
  24. 333
  25. 39
  26. 30
  27. 15
  28. 5
  29. 2
  30. 66
  31. 27
  32. 3
  33. 594
  34. 8
  35. 17
  36. 69
  37. 585
  38. 414
  39. 9
  40. 603

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