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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 462 · 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 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) 22 (c) 198 (d) 66
  2. 2.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) 471 (c) 462 (d) 472
  3. 3.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 120 (c) 110 (d) 119
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 16 (b) 5 (c) 15 (d) 17
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 4 (b) 16 (c) 14 (d) 15
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 19 (b) 18 (c) 17 (d) 8
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 4 (b) 13 (c) 14 (d) 15
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 20 (b) 21 (c) 9 (d) 19
  9. 9.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 14 (d) 7
  10. 10.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 17 (b) 19 (c) 7 (d) 18
  12. 12.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 167 (b) 158 (c) 176 (d) 168
  13. 13.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) 23 (b) 69 (c) 72 (d) 207
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 3 (b) 2 (c) 4 (d) 5
  15. 15.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 47 (c) 38 (d) 48
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 18 (b) 16 (c) 17 (d) 6
  17. 17.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 559 (c) 549 (d) 444
  18. 18.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) 39 (b) 42 (c) 13 (d) 117
  19. 19.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) 18 (b) 54 (c) 57 (d) 162
  20. 20.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
  21. 21.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 363 (c) 314 (d) 354
  22. 22.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 114 (c) 105 (d) 106
  23. 23.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 478 (b) 390 (c) 468 (d) 477
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 2 (b) 4 (c) 3 (d) 5
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 93? (a) 20 (b) 9 (c) 19 (d) 18
  26. 26.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) 45 (b) 15 (c) 18 (d) 5
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 73? (a) 16 (b) 18 (c) 17 (d) 7
  28. 28.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) 51 (c) 54 (d) 153
  29. 29.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  30. 30.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 72? (a) 6 (b) 8 (c) 5 (d) 7
  32. 32.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 219 (c) 229 (d) 224
  33. 33.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  34. 34.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 595 (c) 468 (d) 585
  35. 35.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 446 (c) 562 (d) 552
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 10 (b) 8 (c) 11 (d) 5
  37. 37.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  38. 38.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 18 (b) 19 (c) 20 (d) 9
  40. 40.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) 30 (d) 33

Answer key

  1. 66
  2. 471
  3. 119
  4. 16
  5. 15
  6. 18
  7. 14
  8. 20
  9. 6
  10. 5
  11. 18
  12. 167
  13. 69
  14. 4
  15. 47
  16. 17
  17. 558
  18. 39
  19. 54
  20. 63
  21. 363
  22. 105
  23. 477
  24. 4
  25. 19
  26. 15
  27. 17
  28. 51
  29. 4
  30. 9
  31. 7
  32. 228
  33. 6
  34. 594
  35. 561
  36. 10
  37. 8
  38. 3
  39. 19
  40. 30

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