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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 815 · 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 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) 21 (b) 24 (c) 7 (d) 63
  2. 2.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 139 (c) 148 (d) 140
  3. 3.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 225 (b) 234 (c) 235 (d) 228
  4. 4.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) 54 (b) 57 (c) 18 (d) 162
  5. 5.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) 57 (d) 171
  6. 6.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) 429 (c) 420 (d) 430
  7. 7.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 482 (b) 615 (c) 606 (d) 616
  8. 8.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
  9. 9.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) 153 (b) 54 (c) 17 (d) 51
  10. 10.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
  11. 11.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 104 (c) 86 (d) 95
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 6 (d) 10
  13. 13.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 426 (c) 427 (d) 356
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 8 (b) 17 (c) 19 (d) 18
  15. 15.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 231 (c) 226 (d) 232
  16. 16.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) 27 (b) 24 (c) 72 (d) 8
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 11 (b) 9 (c) 10 (d) 8
  18. 18.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 229 (c) 224 (d) 228
  19. 19.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 577 (b) 576 (c) 567 (d) 456
  20. 20.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) 207 (b) 72 (c) 69 (d) 23
  21. 21.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 178 (c) 188 (d) 187
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 2 (b) 3 (c) 5 (d) 4
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 16 (b) 18 (c) 6 (d) 17
  24. 24.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) 42 (b) 117 (c) 39 (d) 13
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 14 (b) 15 (c) 4 (d) 16
  26. 26.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 288 (c) 315 (d) 325
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 19 (b) 9 (c) 21 (d) 20
  28. 28.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 148 (c) 147 (d) 138
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 7 (b) 19 (c) 18 (d) 17
  30. 30.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 15 (b) 16 (c) 14 (d) 4
  32. 32.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) 15 (c) 135 (d) 45
  33. 33.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
  34. 34.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 9 (c) 81 (d) 30
  35. 35.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 279 (c) 288 (d) 289
  36. 36.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 43 (b) 34 (c) 44 (d) 52
  37. 37.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 85 (b) 86 (c) 76 (d) 94
  38. 38.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 266 (b) 292 (c) 291 (d) 282
  39. 39.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 17 (b) 16 (c) 18 (d) 7

Answer key

  1. 21
  2. 139
  3. 234
  4. 54
  5. 57
  6. 429
  7. 615
  8. 3
  9. 51
  10. 540
  11. 95
  12. 5
  13. 426
  14. 18
  15. 231
  16. 24
  17. 10
  18. 228
  19. 576
  20. 69
  21. 187
  22. 4
  23. 17
  24. 39
  25. 15
  26. 324
  27. 20
  28. 147
  29. 18
  30. 8
  31. 15
  32. 45
  33. 42
  34. 27
  35. 288
  36. 43
  37. 85
  38. 291
  39. 4
  40. 17

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