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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 102 · 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 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 348 (c) 358 (d) 310
  2. 2.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) 33 (c) 11 (d) 36
  3. 3.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 430 (c) 420 (d) 429
  4. 4.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) 153 (c) 51 (d) 54
  5. 5.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 396 (c) 342 (d) 406
  6. 6.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 385 (c) 384 (d) 375
  7. 7.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) 57 (b) 60 (c) 19 (d) 171
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 18 (b) 20 (c) 8 (d) 19
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 8 (b) 9 (c) 12 (d) 11
  10. 10.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 141 (c) 132 (d) 142
  11. 11.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
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 16 (b) 4 (c) 15 (d) 14
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 6 (b) 7 (c) 5 (d) 4
  15. 15.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  16. 16.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  17. 17.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) 39 (d) 40
  18. 18.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 478 (b) 610 (c) 609 (d) 600
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 1 (d) 3
  20. 20.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) 45 (b) 126 (c) 42 (d) 14
  21. 21.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
  22. 22.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  23. 23.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  24. 24.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
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 10 (b) 3 (c) 11 (d) 12
  26. 26.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) 144 (c) 48 (d) 51
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 68? (a) 6 (b) 18 (c) 17 (d) 16
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 5 (b) 6 (c) 3 (d) 4
  29. 29.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 592 (b) 591 (c) 582 (d) 466
  30. 30.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) 66 (c) 22 (d) 198
  31. 31.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 531 (c) 541 (d) 540
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 7 (b) 6 (c) 5 (d) 4
  33. 33.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 595 (c) 594 (d) 585
  34. 34.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 386 (b) 462 (c) 472 (d) 471
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 18 (b) 6 (c) 16 (d) 17
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 74? (a) 8 (b) 6 (c) 7 (d) 5
  37. 37.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 469 (c) 459 (d) 468
  38. 38.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 18 (c) 5 (d) 45
  39. 39.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 343 (b) 342 (c) 333 (d) 300
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 50? (a) 4 (b) 6 (c) 5 (d) 3

Answer key

  1. 357
  2. 33
  3. 429
  4. 51
  5. 405
  6. 384
  7. 57
  8. 19
  9. 11
  10. 141
  11. 45
  12. 15
  13. 8
  14. 6
  15. 9
  16. 4
  17. 39
  18. 609
  19. 3
  20. 42
  21. 8
  22. 4
  23. 7
  24. 24
  25. 11
  26. 48
  27. 17
  28. 5
  29. 591
  30. 66
  31. 540
  32. 6
  33. 594
  34. 471
  35. 17
  36. 7
  37. 468
  38. 15
  39. 342
  40. 5

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