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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 806 · 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) 10 (b) 2 (c) 3 (d) 4
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 66? (a) 16 (b) 17 (c) 18 (d) 6
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 69? (a) 18 (b) 16 (c) 6 (d) 17
  4. 4.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 397 (b) 387 (c) 396 (d) 336
  5. 5.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 79 (c) 70 (d) 88
  6. 6.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 167 (c) 176 (d) 158
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 87? (a) 20 (b) 19 (c) 8 (d) 18
  8. 8.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  9. 9.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 336 (c) 302 (d) 345
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 20 (b) 18 (c) 19 (d) 8
  11. 11.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  12. 12.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  13. 13.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 511 (c) 510 (d) 501
  14. 14.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) 27 (c) 81 (d) 9
  15. 15.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 280 (c) 258 (d) 279
  16. 16.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) 13 (b) 39 (c) 117 (d) 42
  17. 17.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) 24 (b) 72 (c) 216 (d) 75
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 7 (b) 4 (c) 5 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 8 (d) 11
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 15 (b) 16 (c) 6 (d) 17
  21. 21.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  22. 22.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) 51 (d) 17
  23. 23.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 42 (c) 41 (d) 50
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 6 (b) 5 (c) 7 (d) 4
  25. 25.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 183 (b) 193 (c) 192 (d) 200
  26. 26.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  27. 27.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 28 (c) 38 (d) 37
  28. 28.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) 434 (c) 544 (d) 543
  29. 29.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 171 (c) 162 (d) 180
  30. 30.The numbers 8 to 16 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) 12 (c) 36 (d) 108
  31. 31.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 118 (c) 100 (d) 109
  32. 32.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) 63 (b) 21 (c) 24 (d) 7
  33. 33.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 112 (c) 111 (d) 102
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 16 (b) 14 (c) 15 (d) 4
  35. 35.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) 135 (b) 15 (c) 45 (d) 48
  36. 36.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
  37. 37.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 290 (b) 328 (c) 327 (d) 318
  38. 38.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 585 (c) 595 (d) 594
  39. 39.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) 90 (b) 33 (c) 30 (d) 10
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 45? (a) 3 (b) 2 (c) 5 (d) 4

Answer key

  1. 3
  2. 17
  3. 17
  4. 396
  5. 79
  6. 167
  7. 19
  8. 6
  9. 345
  10. 19
  11. 7
  12. 6
  13. 510
  14. 27
  15. 279
  16. 39
  17. 72
  18. 6
  19. 9
  20. 16
  21. 4
  22. 51
  23. 41
  24. 6
  25. 192
  26. 4
  27. 37
  28. 543
  29. 171
  30. 36
  31. 109
  32. 21
  33. 111
  34. 15
  35. 45
  36. 8
  37. 327
  38. 594
  39. 30
  40. 4

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