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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 14 · 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 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 52 (c) 51 (d) 42
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 43? (a) 2 (b) 5 (c) 3 (d) 4
  3. 3.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) 15 (b) 45 (c) 5 (d) 18
  4. 4.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) 135 (b) 48 (c) 45 (d) 15
  5. 5.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) 207 (b) 23 (c) 72 (d) 69
  6. 6.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 349 (b) 339 (c) 304 (d) 348
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 5 (b) 4 (c) 6 (d) 3
  8. 8.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) 27 (b) 24 (c) 72 (d) 8
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 60? (a) 6 (b) 17 (c) 15 (d) 16
  10. 10.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 374 (c) 453 (d) 454
  11. 11.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) 39 (d) 42
  12. 12.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 77 (c) 86 (d) 78
  13. 13.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) 66 (b) 21 (c) 63 (d) 189
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 18 (b) 7 (c) 19 (d) 17
  15. 15.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 19 (b) 9 (c) 18 (d) 20
  17. 17.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 270 (c) 298 (d) 297
  18. 18.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 4 (d) 17
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 8 (b) 17 (c) 18 (d) 19
  20. 20.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 31? (a) 1 (b) 2 (c) 3 (d) 4
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  23. 23.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 3 (d) 5
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 5 (b) 2 (c) 3 (d) 4
  25. 25.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) 11 (b) 99 (c) 33 (d) 36
  26. 26.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 175 (b) 166 (c) 176 (d) 184
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 19 (b) 8 (c) 17 (d) 18
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 8 (b) 20 (c) 19 (d) 18
  29. 29.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 9 (d) 19
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 64? (a) 6 (b) 17 (c) 15 (d) 16
  32. 32.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 146 (c) 145 (d) 154
  33. 33.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
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 15 (b) 4 (c) 13 (d) 14
  35. 35.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  36. 36.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 179 (b) 170 (c) 180 (d) 188
  37. 37.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) 513 (c) 514 (d) 504
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 3 (b) 2 (c) 4 (d) 5
  39. 39.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 397 (b) 387 (c) 396 (d) 336
  40. 40.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 9 (d) 7

Answer key

  1. 51
  2. 4
  3. 15
  4. 45
  5. 69
  6. 348
  7. 5
  8. 24
  9. 16
  10. 453
  11. 39
  12. 77
  13. 63
  14. 18
  15. 4
  16. 19
  17. 297
  18. 3
  19. 18
  20. 9
  21. 3
  22. 2
  23. 4
  24. 4
  25. 33
  26. 175
  27. 18
  28. 19
  29. 6
  30. 19
  31. 16
  32. 145
  33. 42
  34. 14
  35. 5
  36. 179
  37. 513
  38. 4
  39. 396
  40. 8

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