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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 343 · 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 2 written when you write all the numbers from 1 to 39? (a) 14 (b) 15 (c) 13 (d) 3
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 4 (b) 6 (c) 7 (d) 5
  3. 3.The numbers 19 to 27 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) 72 (c) 23 (d) 207
  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) 51 (b) 153 (c) 17 (d) 54
  5. 5.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 453 (c) 454 (d) 374
  6. 6.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 387 (c) 397 (d) 396
  7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 20 (b) 19 (c) 18 (d) 8
  8. 8.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) 10 (b) 90 (c) 33 (d) 30
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 77? (a) 7 (b) 8 (c) 6 (d) 5
  10. 10.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 286 (c) 262 (d) 285
  11. 11.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 481 (b) 392 (c) 471 (d) 480
  12. 12.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 352 (c) 421 (d) 411
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
  14. 14.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 16 (b) 7 (c) 17 (d) 18
  16. 16.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 86 (c) 85 (d) 94
  17. 17.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) 14 (c) 126 (d) 42
  18. 18.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 242 (c) 256 (d) 255
  19. 19.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 523 (c) 522 (d) 513
  20. 20.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5
  21. 21.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) 466 (c) 591 (d) 582
  22. 22.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 99 (b) 100 (c) 108 (d) 90
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 13 (b) 16 (c) 8 (d) 15
  24. 24.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) 162 (b) 54 (c) 18 (d) 57
  25. 25.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 42 (c) 117 (d) 39
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 18 (b) 8 (c) 17 (d) 19
  27. 27.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  28. 28.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 5 (b) 4 (c) 7 (d) 6
  30. 30.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) 63 (b) 7 (c) 21 (d) 24
  31. 31.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) 5 (b) 45 (c) 18 (d) 15
  32. 32.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) 19 (b) 171 (c) 57 (d) 60
  33. 33.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) 60 (b) 63 (c) 180 (d) 20
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 13 (b) 14 (c) 3 (d) 15
  35. 35.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 349 (c) 348 (d) 304
  36. 36.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 51 (c) 42 (d) 52
  37. 37.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) 144 (b) 48 (c) 16 (d) 51
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 14 (b) 16 (c) 5 (d) 15
  39. 39.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 9 (b) 19 (c) 18 (d) 20

Answer key

  1. 14
  2. 6
  3. 69
  4. 51
  5. 453
  6. 396
  7. 19
  8. 30
  9. 7
  10. 285
  11. 480
  12. 420
  13. 8
  14. 5
  15. 17
  16. 85
  17. 42
  18. 255
  19. 522
  20. 6
  21. 591
  22. 99
  23. 15
  24. 54
  25. 39
  26. 18
  27. 5
  28. 9
  29. 6
  30. 21
  31. 15
  32. 57
  33. 60
  34. 14
  35. 348
  36. 51
  37. 48
  38. 15
  39. 8
  40. 19

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