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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 241 · 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 3 written when you write all the numbers from 1 to 81? (a) 8 (b) 19 (c) 18 (d) 17
  2. 2.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) 17 (d) 54
  3. 3.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 1 (d) 3
  4. 4.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
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 6 (b) 16 (c) 18 (d) 17
  6. 6.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) 90 (b) 33 (c) 10 (d) 30
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 12 (b) 10 (c) 13 (d) 7
  8. 8.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) 11 (c) 99 (d) 36
  9. 9.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10
  10. 10.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) 45 (d) 15
  11. 11.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) 157 (c) 166 (d) 148
  12. 12.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) 16 (b) 48 (c) 51 (d) 144
  13. 13.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 10 (d) 11
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 92? (a) 19 (b) 20 (c) 9 (d) 18
  15. 15.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) 19 (c) 60 (d) 57
  16. 16.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 447 (c) 457 (d) 456
  17. 17.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) 6 (b) 21 (c) 18 (d) 54
  18. 18.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 559 (b) 444 (c) 549 (d) 558
  19. 19.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
  20. 20.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  21. 21.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
  22. 22.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 393 (c) 394 (d) 384
  23. 23.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 7 (d) 10
  24. 24.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) 501 (c) 492 (d) 502
  25. 25.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 172 (c) 181 (d) 190
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 6 (b) 17 (c) 16 (d) 18
  27. 27.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 266 (b) 282 (c) 292 (d) 291
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 3 (b) 6 (c) 4 (d) 7
  29. 29.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 290 (c) 327 (d) 318
  30. 30.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) 27 (d) 30
  31. 31.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 544 (b) 534 (c) 543 (d) 434
  32. 32.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 340 (c) 298 (d) 330
  33. 33.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 270 (c) 297 (d) 288
  34. 34.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) 54 (b) 162 (c) 57 (d) 18
  35. 35.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) 60 (c) 180 (d) 20
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 54? (a) 3 (b) 4 (c) 6 (d) 5
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 56? (a) 4 (b) 3 (c) 5 (d) 6
  38. 38.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 4 (b) 15 (c) 14 (d) 16
  40. 40.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

Answer key

  1. 18
  2. 51
  3. 2
  4. 4
  5. 17
  6. 30
  7. 12
  8. 33
  9. 8
  10. 45
  11. 157
  12. 48
  13. 9
  14. 19
  15. 57
  16. 456
  17. 18
  18. 558
  19. 7
  20. 5
  21. 7
  22. 393
  23. 6
  24. 501
  25. 181
  26. 17
  27. 291
  28. 6
  29. 327
  30. 27
  31. 543
  32. 339
  33. 297
  34. 54
  35. 60
  36. 5
  37. 5
  38. 4
  39. 15
  40. 63

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