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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 782 · 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.

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  1. 1.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 66 (c) 58 (d) 57
  2. 2.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 4 (b) 14 (c) 16 (d) 15
  4. 4.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) 8 (b) 24 (c) 72 (d) 27
  5. 5.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 133 (c) 142 (d) 134
  6. 6.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 9 (d) 11
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 5 (b) 15 (c) 17 (d) 16
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 18 (b) 9 (c) 20 (d) 19
  9. 9.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) 45 (b) 48 (c) 15 (d) 135
  10. 10.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 169 (c) 178 (d) 170
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 7 (b) 10 (c) 9 (d) 8
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 5 (b) 4 (c) 6 (d) 7
  13. 13.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 308 (c) 354 (d) 355
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 4 (b) 1 (c) 3 (d) 2
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 4 (d) 5
  16. 16.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 173 (c) 174 (d) 164
  17. 17.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
  18. 18.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 547 (c) 546 (d) 537
  19. 19.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 118 (c) 128 (d) 127
  20. 20.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 111 (b) 120 (c) 112 (d) 102
  21. 21.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 9 (d) 19
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 20 (b) 18 (c) 19 (d) 8
  24. 24.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) 33 (c) 36 (d) 99
  25. 25.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  26. 26.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 18 (b) 7 (c) 19 (d) 17
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 2 (b) 3 (c) 4 (d) 5
  29. 29.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) 75 (c) 72 (d) 24
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 3 (b) 2 (c) 4 (d) 1
  31. 31.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 5 (b) 7 (c) 8 (d) 6
  33. 33.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 501 (b) 412 (c) 511 (d) 510
  34. 34.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) 10 (c) 30 (d) 90
  35. 35.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) 108 (b) 12 (c) 39 (d) 36
  36. 36.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 549 (b) 438 (c) 540 (d) 550
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 66? (a) 13 (b) 15 (c) 6 (d) 14
  38. 38.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 487 (b) 486 (c) 477 (d) 396
  39. 39.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) 42 (c) 39 (d) 13
  40. 40.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8

Answer key

  1. 57
  2. 7
  3. 15
  4. 24
  5. 133
  6. 9
  7. 16
  8. 19
  9. 45
  10. 169
  11. 9
  12. 6
  13. 354
  14. 3
  15. 4
  16. 173
  17. 15
  18. 546
  19. 127
  20. 111
  21. 4
  22. 19
  23. 19
  24. 33
  25. 5
  26. 2
  27. 18
  28. 4
  29. 72
  30. 3
  31. 3
  32. 7
  33. 510
  34. 30
  35. 36
  36. 549
  37. 14
  38. 486
  39. 39
  40. 9

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