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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 955 · 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.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
  2. 2.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) 21 (b) 189 (c) 63 (d) 66
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 14 (b) 16 (c) 15 (d) 5
  4. 4.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 128 (c) 119 (d) 120
  5. 5.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 568 (b) 567 (c) 450 (d) 558
  6. 6.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  7. 7.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) 20 (d) 180
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 86? (a) 19 (b) 20 (c) 18 (d) 8
  9. 9.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 526 (c) 422 (d) 525
  10. 10.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 155 (b) 146 (c) 156 (d) 164
  11. 11.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) 10 (c) 30 (d) 33
  12. 12.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 318 (c) 370 (d) 360
  13. 13.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 295 (b) 294 (c) 268 (d) 285
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 80? (a) 8 (b) 6 (c) 7 (d) 9
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 92? (a) 9 (b) 18 (c) 19 (d) 20
  16. 16.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 296 (b) 327 (c) 337 (d) 336
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 8 (b) 17 (c) 19 (d) 18
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 3 (b) 4 (c) 5 (d) 6
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 18 (b) 16 (c) 7 (d) 17
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 18 (b) 19 (c) 20 (d) 8
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 16 (b) 14 (c) 15 (d) 4
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 20 (b) 18 (c) 19 (d) 8
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 18 (b) 8 (c) 19 (d) 17
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 20 (b) 19 (c) 9 (d) 18
  25. 25.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 6 (b) 4 (c) 3 (d) 5
  27. 27.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 189 (c) 190 (d) 180
  28. 28.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 382 (c) 466 (d) 465
  29. 29.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
  30. 30.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 68 (c) 59 (d) 60
  31. 31.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 17 (b) 18 (c) 19 (d) 7
  33. 33.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7
  34. 34.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 225 (c) 235 (d) 228
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 20 (b) 18 (c) 19 (d) 8
  36. 36.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 634 (c) 624 (d) 494
  37. 37.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  38. 38.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 555 (c) 564 (d) 565
  39. 39.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 4 (b) 7 (c) 6 (d) 5

Answer key

  1. 42
  2. 63
  3. 15
  4. 119
  5. 567
  6. 2
  7. 60
  8. 19
  9. 525
  10. 155
  11. 30
  12. 369
  13. 294
  14. 8
  15. 19
  16. 336
  17. 18
  18. 5
  19. 17
  20. 19
  21. 15
  22. 19
  23. 18
  24. 19
  25. 5
  26. 5
  27. 189
  28. 465
  29. 21
  30. 59
  31. 9
  32. 18
  33. 6
  34. 234
  35. 19
  36. 633
  37. 4
  38. 564
  39. 6
  40. 6

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