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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 448 · 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.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) 17 (b) 153 (c) 51 (d) 54
  2. 2.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 18 (b) 19 (c) 20 (d) 9
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 2 (b) 5 (c) 4 (d) 3
  5. 5.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
  6. 6.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 618 (c) 628 (d) 490
  7. 7.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  8. 8.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  9. 9.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 185 (c) 186 (d) 194
  10. 10.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) 21 (b) 63 (c) 66 (d) 189
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 2 (b) 1 (c) 4 (d) 3
  12. 12.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) 48 (d) 135
  13. 13.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 236 (b) 246 (c) 247 (d) 237
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 17 (b) 6 (c) 18 (d) 16
  15. 15.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 283 (c) 282 (d) 260
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 16 (b) 14 (c) 15 (d) 4
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 20 (b) 9 (c) 21 (d) 19
  18. 18.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 433 (c) 432 (d) 423
  19. 19.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  20. 20.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 526 (b) 422 (c) 525 (d) 516
  21. 21.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 483 (c) 474 (d) 484
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 4 (b) 5 (c) 3 (d) 2
  23. 23.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) 72 (c) 8 (d) 24
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 20 (b) 19 (c) 21 (d) 9
  25. 25.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  26. 26.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  27. 27.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
  28. 28.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 5 (b) 6 (c) 7 (d) 8
  30. 30.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  31. 31.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) 15 (d) 45
  32. 32.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 414 (c) 405 (d) 415
  33. 33.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 155 (c) 164 (d) 146
  34. 34.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 102 (c) 112 (d) 111
  35. 35.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 372 (c) 451 (d) 441
  36. 36.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) 42 (b) 126 (c) 14 (d) 45
  37. 37.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) 23 (d) 207
  38. 38.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 271 (b) 270 (c) 261 (d) 252
  39. 39.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) 81 (c) 9 (d) 27
  40. 40.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6

Answer key

  1. 51
  2. 4
  3. 19
  4. 4
  5. 5
  6. 627
  7. 3
  8. 6
  9. 185
  10. 63
  11. 3
  12. 45
  13. 246
  14. 17
  15. 282
  16. 15
  17. 20
  18. 432
  19. 2
  20. 525
  21. 483
  22. 4
  23. 24
  24. 20
  25. 4
  26. 9
  27. 5
  28. 2
  29. 7
  30. 9
  31. 15
  32. 414
  33. 155
  34. 111
  35. 450
  36. 42
  37. 69
  38. 270
  39. 27
  40. 7

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