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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 615 · 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 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 133 (b) 134 (c) 142 (d) 124
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 13 (b) 14 (c) 4 (d) 15
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 20 (b) 19 (c) 21 (d) 9
  4. 4.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) 45 (b) 5 (c) 15 (d) 18
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 18 (b) 6 (c) 16 (d) 17
  6. 6.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 176 (c) 167 (d) 158
  7. 7.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 19 (b) 18 (c) 7 (d) 17
  9. 9.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) 27 (d) 81
  10. 10.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  11. 11.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 147 (c) 156 (d) 138
  12. 12.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) 162 (b) 18 (c) 54 (d) 57
  13. 13.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 75 (b) 72 (c) 24 (d) 216
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 16 (b) 4 (c) 14 (d) 15
  15. 15.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 378 (c) 450 (d) 459
  16. 16.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 621 (c) 622 (d) 486
  17. 17.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 4 (b) 2 (c) 3 (d) 5
  19. 19.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 481 (b) 392 (c) 480 (d) 471
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 9 (d) 20
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 9 (b) 6 (c) 7 (d) 8
  22. 22.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 435 (c) 436 (d) 362
  23. 23.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 184 (c) 175 (d) 176
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 63? (a) 6 (b) 4 (c) 7 (d) 5
  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.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 65? (a) 7 (b) 5 (c) 4 (d) 6
  28. 28.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) 69 (d) 72
  29. 29.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  30. 30.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 585 (c) 594 (d) 595
  31. 31.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
  32. 32.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 428 (b) 535 (c) 525 (d) 534
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 3 (b) 4 (c) 2 (d) 5
  34. 34.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 540 (b) 531 (c) 432 (d) 541
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 88? (a) 20 (b) 8 (c) 18 (d) 19
  36. 36.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 7 (d) 8
  37. 37.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) 153 (b) 54 (c) 51 (d) 17
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 13 (b) 3 (c) 15 (d) 14
  39. 39.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) 20 (b) 180 (c) 60 (d) 63
  40. 40.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) 126 (b) 14 (c) 45 (d) 42

Answer key

  1. 133
  2. 14
  3. 20
  4. 15
  5. 17
  6. 167
  7. 2
  8. 18
  9. 27
  10. 8
  11. 147
  12. 54
  13. 72
  14. 15
  15. 459
  16. 621
  17. 9
  18. 4
  19. 480
  20. 20
  21. 8
  22. 435
  23. 175
  24. 6
  25. 39
  26. 7
  27. 6
  28. 69
  29. 3
  30. 594
  31. 45
  32. 534
  33. 4
  34. 540
  35. 19
  36. 7
  37. 51
  38. 14
  39. 60
  40. 42

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