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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 255 · 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 13? (a) 5 (b) 6 (c) 14 (d) 7
  2. 2.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) 24 (c) 72 (d) 27
  3. 3.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 414 (c) 348 (d) 415
  4. 4.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 404 (c) 499 (d) 498
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 7 (b) 9 (c) 6 (d) 8
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 15 (b) 14 (c) 16 (d) 4
  7. 7.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) 63 (b) 21 (c) 189 (d) 66
  8. 8.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 334 (c) 394 (d) 393
  9. 9.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 10 (d) 9
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 71? (a) 18 (b) 17 (c) 16 (d) 7
  12. 12.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) 7 (b) 21 (c) 24 (d) 63
  13. 13.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) 36 (c) 108 (d) 12
  14. 14.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 423 (c) 424 (d) 354
  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) 226 (c) 232 (d) 231
  16. 16.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 192 (c) 206 (d) 202
  17. 17.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
  18. 18.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 7 (d) 10
  19. 19.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) 33 (b) 36 (c) 99 (d) 11
  20. 20.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 446 (b) 552 (c) 562 (d) 561
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 3 (b) 2 (c) 5 (d) 4
  22. 22.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  23. 23.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 53 (c) 62 (d) 54
  24. 24.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) 21 (b) 6 (c) 18 (d) 54
  25. 25.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) 60 (c) 59 (d) 50
  26. 26.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 16 (b) 17 (c) 6 (d) 18
  28. 28.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 571 (c) 570 (d) 452
  29. 29.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) 30 (c) 33 (d) 10
  30. 30.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) 22 (b) 198 (c) 66 (d) 69
  31. 31.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  32. 32.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 97 (c) 88 (d) 106
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 18 (b) 20 (c) 8 (d) 19
  34. 34.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 223 (b) 213 (c) 222 (d) 220
  35. 35.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 110 (c) 100 (d) 109
  36. 36.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  37. 37.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 56 (c) 38 (d) 47
  38. 38.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  39. 39.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) 51 (c) 54 (d) 17
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 17 (b) 6 (c) 18 (d) 16

Answer key

  1. 6
  2. 24
  3. 414
  4. 498
  5. 8
  6. 15
  7. 63
  8. 393
  9. 8
  10. 3
  11. 17
  12. 21
  13. 36
  14. 423
  15. 231
  16. 201
  17. 4
  18. 6
  19. 33
  20. 561
  21. 4
  22. 5
  23. 53
  24. 18
  25. 59
  26. 4
  27. 17
  28. 570
  29. 30
  30. 66
  31. 7
  32. 97
  33. 19
  34. 222
  35. 109
  36. 2
  37. 47
  38. 9
  39. 51
  40. 17

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