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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 433 · 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 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) 42 (b) 45 (c) 126 (d) 14
  2. 2.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 12 (d) 9
  3. 3.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  4. 4.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 50 (c) 60 (d) 59
  5. 5.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 8 (d) 6
  6. 6.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 101 (b) 102 (c) 110 (d) 92
  7. 7.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) 99 (c) 33 (d) 11
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 8 (b) 17 (c) 19 (d) 18
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 18 (b) 8 (c) 19 (d) 20
  10. 10.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 290 (c) 318 (d) 328
  11. 11.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) 8 (b) 27 (c) 72 (d) 24
  12. 12.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 420 (c) 352 (d) 421
  13. 13.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) 117 (d) 13
  14. 14.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 6 (d) 15
  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) 15 (b) 5 (c) 18 (d) 45
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 93? (a) 20 (b) 19 (c) 9 (d) 18
  17. 17.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  18. 18.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
  19. 19.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  20. 20.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) 57 (c) 54 (d) 162
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 8 (b) 19 (c) 20 (d) 18
  22. 22.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 73 (c) 64 (d) 82
  23. 23.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 96 (c) 105 (d) 106
  24. 24.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  25. 25.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
  26. 26.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) 7 (c) 63 (d) 24
  27. 27.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 166 (c) 157 (d) 148
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 2 (b) 3 (c) 1 (d) 4
  29. 29.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 238 (b) 249 (c) 240 (d) 250
  30. 30.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 384 (c) 393 (d) 394
  31. 31.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  32. 32.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 116 (c) 115 (d) 106
  33. 33.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 369 (c) 318 (d) 360
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 92? (a) 9 (b) 19 (c) 20 (d) 21
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 62? (a) 5 (b) 6 (c) 7 (d) 4
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 6 (b) 15 (c) 17 (d) 16
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 8 (b) 19 (c) 20 (d) 18
  38. 38.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 307 (c) 306 (d) 297
  39. 39.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 337 (b) 327 (c) 296 (d) 336
  40. 40.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 248 (c) 264 (d) 265

Answer key

  1. 42
  2. 8
  3. 6
  4. 59
  5. 7
  6. 101
  7. 33
  8. 18
  9. 19
  10. 327
  11. 24
  12. 420
  13. 39
  14. 5
  15. 15
  16. 19
  17. 5
  18. 3
  19. 2
  20. 54
  21. 19
  22. 73
  23. 105
  24. 8
  25. 4
  26. 21
  27. 157
  28. 3
  29. 249
  30. 393
  31. 9
  32. 115
  33. 369
  34. 20
  35. 6
  36. 16
  37. 19
  38. 306
  39. 336
  40. 264

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