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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 961 · 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.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 261 (c) 262 (d) 252
  2. 2.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 3 (d) 10
  3. 3.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 271 (b) 261 (c) 270 (d) 252
  4. 4.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  5. 5.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  6. 6.The numbers 2 to 10 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) 6 (c) 21 (d) 18
  7. 7.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  8. 8.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 232 (c) 226 (d) 222
  9. 9.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 75 (b) 24 (c) 216 (d) 72
  10. 10.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 440 (b) 553 (c) 543 (d) 552
  11. 11.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 332 (b) 381 (c) 391 (d) 390
  12. 12.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 158 (c) 149 (d) 150
  13. 13.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) 126 (c) 14 (d) 42
  14. 14.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 172 (c) 171 (d) 162
  15. 15.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 147 (b) 148 (c) 156 (d) 138
  16. 16.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  17. 17.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) 99 (b) 33 (c) 11 (d) 36
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 93? (a) 20 (b) 9 (c) 18 (d) 19
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 91? (a) 9 (b) 10 (c) 12 (d) 11
  20. 20.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 87 (b) 78 (c) 88 (d) 96
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 4 (b) 5 (c) 3 (d) 2
  22. 22.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 131 (c) 140 (d) 122
  23. 23.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) 57 (b) 54 (c) 18 (d) 162
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 3 (b) 4 (c) 6 (d) 5
  25. 25.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) 15 (d) 5
  26. 26.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
  27. 27.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 225 (c) 216 (d) 226
  28. 28.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 17 (d) 3
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 84? (a) 19 (b) 8 (c) 18 (d) 17
  30. 30.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) 72 (b) 8 (c) 27 (d) 24
  31. 31.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 403 (b) 393 (c) 402 (d) 340
  32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 19 (b) 18 (c) 17 (d) 8
  33. 33.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 18 (b) 17 (c) 7 (d) 16
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 17 (b) 16 (c) 18 (d) 7
  36. 36.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) 266 (c) 282 (d) 292
  37. 37.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 18 (b) 16 (c) 17 (d) 6
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 13 (b) 14 (c) 15 (d) 3
  40. 40.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 372 (c) 451 (d) 441

Answer key

  1. 261
  2. 4
  3. 270
  4. 3
  5. 5
  6. 18
  7. 6
  8. 231
  9. 72
  10. 552
  11. 390
  12. 149
  13. 42
  14. 171
  15. 147
  16. 2
  17. 33
  18. 19
  19. 11
  20. 87
  21. 4
  22. 131
  23. 54
  24. 5
  25. 15
  26. 6
  27. 225
  28. 3
  29. 18
  30. 24
  31. 402
  32. 18
  33. 4
  34. 17
  35. 17
  36. 291
  37. 5
  38. 17
  39. 14
  40. 450

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