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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 911 · 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 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 238 (b) 240 (c) 249 (d) 250
  2. 2.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 33 (c) 34 (d) 24
  3. 3.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
  4. 4.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) 12 (c) 36 (d) 108
  5. 5.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 283 (b) 273 (c) 282 (d) 260
  6. 6.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 83 (c) 84 (d) 92
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 3 (b) 2 (c) 4 (d) 1
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 6 (b) 17 (c) 16 (d) 18
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 90? (a) 18 (b) 20 (c) 9 (d) 19
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 11 (b) 10 (c) 3 (d) 12
  11. 11.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 72 (c) 81 (d) 82
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
  13. 13.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 589 (b) 588 (c) 579 (d) 464
  14. 14.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
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 8 (b) 19 (c) 20 (d) 18
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 3 (d) 2
  17. 17.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 324 (c) 334 (d) 294
  18. 18.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) 72 (b) 24 (c) 8 (d) 27
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 20 (b) 19 (c) 9 (d) 18
  20. 20.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) 63 (b) 21 (c) 189 (d) 66
  21. 21.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) 24 (b) 63 (c) 21 (d) 7
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 3 (b) 5 (c) 4 (d) 2
  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) 396 (b) 336 (c) 387 (d) 397
  24. 24.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
  25. 25.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 574 (b) 573 (c) 454 (d) 564
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 14 (b) 15 (c) 13 (d) 3
  27. 27.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 128 (c) 146 (d) 137
  28. 28.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 5 (d) 7
  29. 29.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
  30. 30.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) 51 (d) 48
  31. 31.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 94 (c) 85 (d) 86
  32. 32.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 3 (d) 10
  33. 33.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 48 (c) 66 (d) 57
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 61? (a) 5 (b) 7 (c) 4 (d) 6
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 9 (b) 8 (c) 11 (d) 10
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 12 (b) 13 (c) 9 (d) 10
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 9 (b) 16 (c) 15 (d) 13
  38. 38.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 22 (c) 198 (d) 66
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 3 (b) 15 (c) 14 (d) 13
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 92? (a) 21 (b) 19 (c) 9 (d) 20

Answer key

  1. 249
  2. 33
  3. 8
  4. 36
  5. 282
  6. 83
  7. 3
  8. 17
  9. 19
  10. 11
  11. 81
  12. 9
  13. 588
  14. 72
  15. 19
  16. 3
  17. 333
  18. 24
  19. 19
  20. 63
  21. 21
  22. 4
  23. 396
  24. 8
  25. 573
  26. 14
  27. 137
  28. 6
  29. 5
  30. 48
  31. 85
  32. 4
  33. 57
  34. 6
  35. 10
  36. 12
  37. 15
  38. 66
  39. 14
  40. 20

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