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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 572 · 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.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 4 (b) 6 (c) 5 (d) 7
  2. 2.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) 171 (c) 60 (d) 57
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 16 (b) 15 (c) 17 (d) 5
  4. 4.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) 45 (d) 14
  5. 5.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 2 (d) 18
  6. 6.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 63 (c) 72 (d) 64
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  8. 8.The numbers 14 to 22 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) 162 (c) 57 (d) 54
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 43? (a) 3 (b) 4 (c) 5 (d) 2
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 77? (a) 19 (b) 7 (c) 17 (d) 18
  11. 11.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 230 (b) 238 (c) 228 (d) 237
  12. 12.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 138 (c) 147 (d) 148
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 45? (a) 5 (b) 3 (c) 6 (d) 4
  14. 14.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 583 (b) 582 (c) 460 (d) 573
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 4 (b) 3 (c) 5 (d) 2
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 8 (b) 6 (c) 4 (d) 9
  17. 17.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) 170 (c) 169 (d) 178
  18. 18.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 116 (c) 126 (d) 125
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 7 (b) 5 (c) 8 (d) 6
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 20 (b) 8 (c) 18 (d) 19
  21. 21.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 225 (b) 226 (c) 216 (d) 222
  22. 22.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) 90 (c) 33 (d) 10
  23. 23.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
  24. 24.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 280 (c) 270 (d) 258
  25. 25.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 81 (b) 72 (c) 90 (d) 82
  26. 26.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  27. 27.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) 387 (c) 336 (d) 397
  28. 28.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 292 (c) 291 (d) 266
  29. 29.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 21 (b) 19 (c) 9 (d) 20
  31. 31.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) 135 (b) 15 (c) 48 (d) 45
  32. 32.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) 63 (b) 180 (c) 60 (d) 20
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 4 (b) 5 (c) 6 (d) 3
  34. 34.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 17 (d) 3
  35. 35.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) 189 (b) 63 (c) 21 (d) 66
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 58? (a) 4 (b) 6 (c) 5 (d) 7
  37. 37.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 196 (c) 186 (d) 202
  38. 38.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
  39. 39.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 2 (b) 3 (c) 5 (d) 4

Answer key

  1. 6
  2. 57
  3. 16
  4. 42
  5. 2
  6. 63
  7. 4
  8. 54
  9. 4
  10. 18
  11. 237
  12. 147
  13. 5
  14. 582
  15. 4
  16. 8
  17. 169
  18. 125
  19. 7
  20. 19
  21. 225
  22. 30
  23. 9
  24. 279
  25. 81
  26. 5
  27. 396
  28. 291
  29. 7
  30. 20
  31. 45
  32. 60
  33. 5
  34. 3
  35. 63
  36. 6
  37. 195
  38. 6
  39. 7
  40. 4

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