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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 205 · 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 5? (a) 6 (b) 4 (c) 10 (d) 5
  2. 2.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
  3. 3.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) 21 (c) 18 (d) 6
  4. 4.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 16 (b) 4 (c) 14 (d) 15
  6. 6.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) 180 (b) 63 (c) 20 (d) 60
  7. 7.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) 216 (c) 24 (d) 72
  8. 8.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 459 (c) 468 (d) 469
  9. 9.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 331 (b) 330 (c) 321 (d) 292
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 13 (b) 3 (c) 15 (d) 14
  11. 11.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 537 (c) 436 (d) 547
  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) 21 (b) 63 (c) 7 (d) 24
  13. 13.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) 72 (c) 27 (d) 24
  14. 14.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 172 (c) 164 (d) 163
  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) 45 (b) 18 (c) 5 (d) 15
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 18 (b) 20 (c) 19 (d) 9
  17. 17.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 41 (b) 42 (c) 50 (d) 32
  18. 18.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  19. 19.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 420 (c) 430 (d) 429
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 17 (b) 7 (c) 18 (d) 19
  21. 21.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) 23 (b) 207 (c) 72 (d) 69
  22. 22.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) 48 (b) 15 (c) 45 (d) 135
  23. 23.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 604 (b) 594 (c) 474 (d) 603
  24. 24.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  25. 25.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) 162 (d) 18
  26. 26.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 133 (b) 142 (c) 124 (d) 134
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 9 (b) 3 (c) 10 (d) 8
  29. 29.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 8 (d) 10
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 98? (a) 19 (b) 9 (c) 20 (d) 21
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 16 (b) 17 (c) 18 (d) 6
  32. 32.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 250 (c) 258 (d) 267
  33. 33.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 39 (b) 40 (c) 48 (d) 30
  34. 34.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 54? (a) 3 (b) 6 (c) 5 (d) 4
  36. 36.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  37. 37.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 19 (d) 21
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 55? (a) 16 (b) 17 (c) 15 (d) 5
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 7 (b) 6 (c) 5 (d) 4

Answer key

  1. 5
  2. 3
  3. 18
  4. 9
  5. 15
  6. 60
  7. 72
  8. 468
  9. 330
  10. 14
  11. 546
  12. 21
  13. 24
  14. 163
  15. 15
  16. 19
  17. 41
  18. 4
  19. 429
  20. 18
  21. 69
  22. 45
  23. 603
  24. 6
  25. 54
  26. 133
  27. 2
  28. 9
  29. 9
  30. 20
  31. 17
  32. 267
  33. 39
  34. 4
  35. 5
  36. 7
  37. 3
  38. 20
  39. 16
  40. 6

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