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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 119 · 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 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 432 (c) 442 (d) 441
  2. 2.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 2 (d) 3
  4. 4.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 5 (d) 16
  5. 5.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 16 (b) 144 (c) 48 (d) 51
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 85? (a) 8 (b) 19 (c) 20 (d) 18
  7. 7.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 210 (c) 220 (d) 218
  8. 8.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 535 (b) 534 (c) 525 (d) 428
  9. 9.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 334 (c) 333 (d) 294
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 43? (a) 5 (b) 2 (c) 3 (d) 4
  11. 11.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) 18 (b) 5 (c) 45 (d) 15
  12. 12.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
  13. 13.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  14. 14.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 18 (b) 19 (c) 17 (d) 7
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 2 (b) 3 (c) 5 (d) 4
  17. 17.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 199 (c) 198 (d) 204
  18. 18.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 583 (c) 582 (d) 573
  19. 19.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) 7 (b) 24 (c) 21 (d) 63
  20. 20.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 318 (c) 290 (d) 328
  21. 21.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) 6 (c) 18 (d) 54
  22. 22.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 502 (c) 492 (d) 501
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 99? (a) 21 (b) 9 (c) 20 (d) 19
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 19 (b) 18 (c) 8 (d) 17
  25. 25.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) 216 (b) 72 (c) 24 (d) 75
  26. 26.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 84? (a) 17 (b) 8 (c) 19 (d) 18
  28. 28.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  29. 29.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 10 (d) 1
  30. 30.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 121 (b) 130 (c) 122 (d) 112
  31. 31.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) 19 (b) 57 (c) 60 (d) 171
  32. 32.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 63? (a) 6 (b) 5 (c) 4 (d) 7
  34. 34.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) 117 (b) 39 (c) 13 (d) 42
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 15 (b) 3 (c) 14 (d) 13
  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) 30 (b) 33 (c) 10 (d) 90
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 16 (b) 4 (c) 14 (d) 15
  38. 38.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 108 (c) 12 (d) 36
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 64? (a) 16 (b) 6 (c) 18 (d) 17
  40. 40.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) 72 (b) 69 (c) 207 (d) 23

Answer key

  1. 441
  2. 4
  3. 3
  4. 4
  5. 48
  6. 19
  7. 219
  8. 534
  9. 333
  10. 4
  11. 15
  12. 8
  13. 3
  14. 6
  15. 18
  16. 4
  17. 198
  18. 582
  19. 21
  20. 327
  21. 18
  22. 501
  23. 20
  24. 18
  25. 72
  26. 8
  27. 18
  28. 9
  29. 2
  30. 121
  31. 57
  32. 5
  33. 6
  34. 39
  35. 14
  36. 30
  37. 15
  38. 36
  39. 17
  40. 69

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