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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 326 · 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 two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
  2. 2.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  3. 3.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 332 (c) 391 (d) 390
  4. 4.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) 30 (b) 81 (c) 27 (d) 9
  5. 5.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 24 (b) 34 (c) 33 (d) 42
  6. 6.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) 23 (c) 69 (d) 72
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 5 (b) 4 (c) 6 (d) 3
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 7 (b) 8 (c) 9 (d) 6
  9. 9.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 247 (b) 236 (c) 237 (d) 246
  10. 10.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  11. 11.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 18 (b) 6 (c) 17 (d) 16
  13. 13.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) 66 (b) 189 (c) 21 (d) 63
  14. 14.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 185 (c) 186 (d) 194
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 44? (a) 2 (b) 3 (c) 5 (d) 4
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 6 (b) 17 (c) 18 (d) 16
  17. 17.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 107 (b) 98 (c) 116 (d) 108
  18. 18.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) 16 (b) 48 (c) 144 (d) 51
  19. 19.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
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 52? (a) 5 (b) 16 (c) 14 (d) 15
  21. 21.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 234 (c) 235 (d) 225
  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) 21 (b) 63 (c) 24 (d) 7
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 15 (b) 16 (c) 4 (d) 14
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 19 (b) 20 (c) 9 (d) 21
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 13 (b) 3 (c) 15 (d) 14
  26. 26.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 175 (b) 184 (c) 176 (d) 166
  27. 27.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 282 (c) 266 (d) 292
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 82? (a) 18 (b) 19 (c) 17 (d) 8
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 62? (a) 4 (b) 6 (c) 7 (d) 5
  30. 30.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 18 (b) 6 (c) 17 (d) 16
  32. 32.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) 20 (b) 63 (c) 180 (d) 60
  33. 33.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) 228 (c) 224 (d) 229
  34. 34.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 543 (c) 434 (d) 544
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 4 (b) 3 (c) 5 (d) 6
  36. 36.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
  37. 37.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 286 (c) 285 (d) 276
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 19 (b) 17 (c) 18 (d) 7
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 14 (b) 13 (c) 15 (d) 4
  40. 40.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 118 (c) 117 (d) 108

Answer key

  1. 3
  2. 2
  3. 390
  4. 27
  5. 33
  6. 69
  7. 5
  8. 8
  9. 246
  10. 2
  11. 9
  12. 17
  13. 63
  14. 185
  15. 4
  16. 17
  17. 107
  18. 48
  19. 66
  20. 15
  21. 234
  22. 21
  23. 15
  24. 20
  25. 14
  26. 175
  27. 291
  28. 18
  29. 6
  30. 6
  31. 17
  32. 60
  33. 228
  34. 543
  35. 5
  36. 9
  37. 285
  38. 18
  39. 14
  40. 117

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