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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 187 · 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 4 written when you write all the numbers from 1 to 52? (a) 5 (b) 15 (c) 16 (d) 14
  2. 2.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 120 (c) 129 (d) 130
  3. 3.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 9 (b) 20 (c) 19 (d) 18
  5. 5.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 161 (c) 170 (d) 162
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 8 (b) 18 (c) 20 (d) 19
  7. 7.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 210 (c) 198 (d) 208
  8. 8.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 469 (b) 384 (c) 459 (d) 468
  9. 9.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  10. 10.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 82 (c) 74 (d) 73
  11. 11.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) 27 (d) 72
  12. 12.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) 45 (c) 14 (d) 42
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 18 (b) 6 (c) 17 (d) 16
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 14 (b) 16 (c) 5 (d) 15
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 9 (b) 8 (c) 7 (d) 10
  16. 16.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 367 (c) 316 (d) 366
  17. 17.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 112 (c) 104 (d) 103
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 18 (b) 6 (c) 16 (d) 17
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 58? (a) 5 (b) 4 (c) 7 (d) 6
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 14 (b) 13 (c) 3 (d) 15
  21. 21.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) 51 (b) 153 (c) 54 (d) 17
  22. 22.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
  23. 23.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
  24. 24.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) 7 (b) 63 (c) 21 (d) 24
  25. 25.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 180 (c) 198 (d) 189
  26. 26.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 372 (c) 326 (d) 381
  27. 27.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) 81 (c) 30 (d) 27
  28. 28.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  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) 24 (b) 75 (c) 216 (d) 72
  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) 51 (b) 48 (c) 144 (d) 16
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 6 (b) 7 (c) 4 (d) 5
  32. 32.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) 99 (b) 36 (c) 33 (d) 11
  33. 33.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) 573 (c) 582 (d) 460
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 19 (b) 8 (c) 20 (d) 18
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 15 (b) 9 (c) 17 (d) 18
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 92? (a) 21 (b) 19 (c) 20 (d) 9
  37. 37.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 406 (c) 342 (d) 405
  38. 38.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 193 (b) 192 (c) 200 (d) 183
  39. 39.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 242 (b) 256 (c) 246 (d) 255
  40. 40.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 160 (c) 150 (d) 159

Answer key

  1. 15
  2. 129
  3. 2
  4. 19
  5. 161
  6. 19
  7. 207
  8. 468
  9. 2
  10. 73
  11. 24
  12. 42
  13. 17
  14. 15
  15. 9
  16. 366
  17. 103
  18. 17
  19. 6
  20. 14
  21. 51
  22. 7
  23. 66
  24. 21
  25. 189
  26. 381
  27. 27
  28. 8
  29. 72
  30. 48
  31. 6
  32. 33
  33. 582
  34. 19
  35. 17
  36. 20
  37. 405
  38. 192
  39. 255
  40. 159

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