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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 516 · 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 9 written when you write all the numbers from 1 to 94? (a) 15 (b) 12 (c) 14 (d) 9
  2. 2.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) 66 (b) 69 (c) 22 (d) 198
  3. 3.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 256 (c) 277 (d) 267
  4. 4.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 582 (c) 583 (d) 573
  5. 5.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 230 (b) 237 (c) 228 (d) 238
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 4 (b) 1 (c) 2 (d) 3
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 18 (b) 17 (c) 16 (d) 6
  8. 8.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) 20 (c) 60 (d) 180
  9. 9.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  10. 10.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 351 (c) 243 (d) 234
  11. 11.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 339 (c) 304 (d) 349
  12. 12.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) 142 (c) 132 (d) 141
  13. 13.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 7 (d) 12
  14. 14.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 616 (b) 482 (c) 615 (d) 606
  15. 15.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) 18 (c) 5 (d) 15
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 98? (a) 21 (b) 20 (c) 9 (d) 19
  17. 17.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) 33 (b) 10 (c) 30 (d) 90
  18. 18.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 9 (d) 7
  19. 19.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  20. 20.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 154 (c) 153 (d) 144
  21. 21.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) 36 (b) 11 (c) 99 (d) 33
  22. 22.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) 24 (b) 21 (c) 63 (d) 7
  23. 23.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
  24. 24.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
  25. 25.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 138 (c) 137 (d) 128
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 20 (d) 19
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 97? (a) 19 (b) 21 (c) 20 (d) 9
  28. 28.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  29. 29.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 98 (c) 89 (d) 90
  30. 30.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) 60 (c) 171 (d) 57
  31. 31.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 9 (b) 21 (c) 19 (d) 20
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 12 (b) 14 (c) 13 (d) 3
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 8 (b) 6 (c) 7 (d) 5
  35. 35.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 5 (d) 14
  36. 36.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 613 (c) 612 (d) 603
  37. 37.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  38. 38.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) 45 (b) 48 (c) 135 (d) 15
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 5 (b) 3 (c) 2 (d) 4
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 8 (b) 7 (c) 6 (d) 9

Answer key

  1. 14
  2. 66
  3. 276
  4. 582
  5. 237
  6. 3
  7. 17
  8. 60
  9. 4
  10. 243
  11. 348
  12. 141
  13. 8
  14. 615
  15. 15
  16. 20
  17. 30
  18. 8
  19. 7
  20. 153
  21. 33
  22. 21
  23. 14
  24. 51
  25. 137
  26. 19
  27. 20
  28. 9
  29. 89
  30. 57
  31. 4
  32. 20
  33. 13
  34. 7
  35. 6
  36. 612
  37. 5
  38. 45
  39. 4
  40. 8

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