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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 429 · 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 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) 9 (b) 27 (c) 81 (d) 30
  2. 2.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) 60 (b) 180 (c) 20 (d) 63
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4
  4. 4.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 13 (d) 6
  5. 5.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 58? (a) 4 (b) 5 (c) 3 (d) 6
  7. 7.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 242 (c) 246 (d) 255
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 18 (b) 17 (c) 7 (d) 19
  9. 9.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 63 (b) 64 (c) 54 (d) 72
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 1 (b) 2 (c) 3 (d) 4
  12. 12.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 12 (d) 9
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 78? (a) 18 (b) 7 (c) 19 (d) 17
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 6 (b) 8 (c) 5 (d) 7
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 21 (b) 19 (c) 20 (d) 9
  16. 16.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4
  17. 17.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) 33 (b) 30 (c) 90 (d) 10
  18. 18.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 5 (b) 4 (c) 3 (d) 2
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 15 (b) 5 (c) 16 (d) 17
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 15 (b) 14 (c) 4 (d) 13
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 18 (d) 19
  23. 23.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
  24. 24.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 90 (c) 72 (d) 81
  25. 25.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 588 (b) 579 (c) 464 (d) 589
  26. 26.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) 18 (b) 21 (c) 54 (d) 6
  27. 27.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  28. 28.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 244 (c) 351 (d) 243
  29. 29.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 422 (b) 516 (c) 525 (d) 526
  30. 30.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  31. 31.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 298 (c) 330 (d) 340
  32. 32.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) 13 (c) 42 (d) 39
  33. 33.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) 21 (b) 24 (c) 63 (d) 7
  34. 34.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) 8 (c) 72 (d) 24
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 60? (a) 17 (b) 6 (c) 16 (d) 15
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 3 (b) 6 (c) 4 (d) 5
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 19 (b) 17 (c) 8 (d) 18
  38. 38.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) 42 (c) 14 (d) 45
  39. 39.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 498 (c) 410 (d) 508
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 4 (b) 2 (c) 3 (d) 5

Answer key

  1. 27
  2. 60
  3. 5
  4. 7
  5. 2
  6. 5
  7. 255
  8. 18
  9. 63
  10. 7
  11. 3
  12. 8
  13. 18
  14. 7
  15. 20
  16. 4
  17. 30
  18. 3
  19. 4
  20. 16
  21. 14
  22. 19
  23. 396
  24. 81
  25. 588
  26. 18
  27. 6
  28. 243
  29. 525
  30. 3
  31. 339
  32. 39
  33. 21
  34. 24
  35. 16
  36. 5
  37. 18
  38. 42
  39. 507
  40. 4

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