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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 553 · 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 two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  2. 2.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 378 (c) 460 (d) 459
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 14 (b) 15 (c) 13 (d) 3
  4. 4.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) 36 (b) 33 (c) 11 (d) 99
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 6 (b) 17 (c) 16 (d) 18
  6. 6.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 643 (b) 500 (c) 633 (d) 642
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 17 (b) 6 (c) 16 (d) 18
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  9. 9.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  10. 10.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 268 (c) 258 (d) 267
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 3 (b) 5 (c) 6 (d) 4
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 5 (b) 4 (c) 3 (d) 2
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 85? (a) 9 (b) 7 (c) 8 (d) 6
  14. 14.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
  15. 15.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) 30 (c) 27 (d) 81
  16. 16.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 30 (b) 48 (c) 40 (d) 39
  17. 17.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 94? (a) 20 (b) 19 (c) 21 (d) 9
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 60? (a) 6 (b) 4 (c) 5 (d) 7
  20. 20.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
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 3 (b) 5 (c) 2 (d) 4
  22. 22.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 160 (c) 169 (d) 178
  23. 23.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 52 (c) 44 (d) 43
  24. 24.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 444 (c) 453 (d) 374
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 5 (b) 7 (c) 4 (d) 6
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 8 (b) 11 (c) 9 (d) 10
  27. 27.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) 147 (c) 148 (d) 138
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 14 (b) 3 (c) 15 (d) 13
  29. 29.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) 51 (c) 54 (d) 153
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 12 (b) 11 (c) 6 (d) 9
  31. 31.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) 7 (c) 63 (d) 24
  32. 32.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) 108 (c) 12 (d) 36
  33. 33.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 148 (c) 157 (d) 166
  34. 34.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 553 (c) 440 (d) 552
  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) 21 (b) 66 (c) 63 (d) 189
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 9 (b) 19 (c) 20 (d) 18
  37. 37.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  38. 38.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 68? (a) 18 (b) 6 (c) 17 (d) 16
  40. 40.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 232 (b) 222 (c) 231 (d) 226

Answer key

  1. 6
  2. 459
  3. 14
  4. 33
  5. 17
  6. 642
  7. 17
  8. 5
  9. 3
  10. 267
  11. 5
  12. 4
  13. 8
  14. 3
  15. 27
  16. 39
  17. 2
  18. 20
  19. 6
  20. 30
  21. 4
  22. 169
  23. 43
  24. 453
  25. 6
  26. 10
  27. 147
  28. 14
  29. 51
  30. 11
  31. 21
  32. 36
  33. 157
  34. 552
  35. 63
  36. 19
  37. 6
  38. 7
  39. 17
  40. 231

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