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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 338 · 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 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 504 (b) 514 (c) 414 (d) 513
  2. 2.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 261 (b) 252 (c) 270 (d) 271
  3. 3.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
  4. 4.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 18 (b) 6 (c) 17 (d) 16
  6. 6.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  7. 7.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) 42 (b) 14 (c) 126 (d) 45
  8. 8.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 492 (c) 502 (d) 501
  9. 9.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 420 (c) 513 (d) 523
  10. 10.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) 20 (b) 180 (c) 63 (d) 60
  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) 72 (b) 27 (c) 8 (d) 24
  12. 12.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 154 (c) 146 (d) 145
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 56? (a) 5 (b) 3 (c) 4 (d) 6
  14. 14.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  15. 15.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 246 (c) 262 (d) 261
  16. 16.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 189 (c) 199 (d) 198
  17. 17.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) 48 (b) 135 (c) 15 (d) 45
  18. 18.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 17 (b) 18 (c) 6 (d) 16
  20. 20.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) 33 (b) 99 (c) 11 (d) 36
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 3 (b) 5 (c) 2 (d) 4
  22. 22.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 18 (c) 6 (d) 21
  23. 23.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 369 (c) 324 (d) 379
  24. 24.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) 82 (c) 81 (d) 72
  25. 25.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 307 (c) 306 (d) 276
  26. 26.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) 171 (b) 60 (c) 57 (d) 19
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 14 (b) 3 (c) 13 (d) 12
  28. 28.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) 66 (b) 69 (c) 198 (d) 22
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 88? (a) 8 (b) 18 (c) 20 (d) 19
  30. 30.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 598 (b) 597 (c) 470 (d) 588
  31. 31.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
  32. 32.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 313 (c) 312 (d) 280
  33. 33.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  34. 34.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 342 (c) 343 (d) 300
  35. 35.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 168 (c) 176 (d) 167
  36. 36.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
  37. 37.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 93 (c) 94 (d) 84
  38. 38.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  39. 39.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 18 (b) 9 (c) 20 (d) 19

Answer key

  1. 513
  2. 270
  3. 127
  4. 6
  5. 17
  6. 5
  7. 42
  8. 501
  9. 522
  10. 60
  11. 24
  12. 145
  13. 5
  14. 6
  15. 261
  16. 198
  17. 45
  18. 8
  19. 17
  20. 33
  21. 4
  22. 18
  23. 378
  24. 81
  25. 306
  26. 57
  27. 13
  28. 66
  29. 19
  30. 597
  31. 27
  32. 312
  33. 3
  34. 342
  35. 167
  36. 8
  37. 93
  38. 7
  39. 9
  40. 19

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