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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 258 · 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 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 595 (b) 468 (c) 585 (d) 594
  2. 2.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 70 (c) 61 (d) 62
  3. 3.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 556 (c) 546 (d) 555
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 9 (b) 18 (c) 19 (d) 20
  5. 5.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 2 (b) 5 (c) 4 (d) 3
  7. 7.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 202 (c) 195 (d) 196
  8. 8.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 7 (d) 6
  9. 9.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
  10. 10.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 321 (c) 312 (d) 286
  11. 11.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  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) 63 (c) 21 (d) 24
  13. 13.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) 60 (c) 20 (d) 63
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 6 (b) 16 (c) 18 (d) 17
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 5 (b) 2 (c) 3 (d) 4
  16. 16.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) 66 (b) 21 (c) 63 (d) 189
  17. 17.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 553 (c) 552 (d) 440
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 4 (b) 15 (c) 14 (d) 13
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 13 (b) 15 (c) 14 (d) 3
  20. 20.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 155 (c) 164 (d) 156
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 5 (b) 4 (c) 2 (d) 3
  22. 22.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
  23. 23.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 16 (b) 18 (c) 6 (d) 17
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 4 (b) 16 (c) 15 (d) 14
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 66? (a) 6 (b) 16 (c) 17 (d) 18
  27. 27.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
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 4 (b) 3 (c) 5 (d) 6
  29. 29.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 166 (c) 174 (d) 165
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 82? (a) 8 (b) 19 (c) 17 (d) 18
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 16 (b) 6 (c) 17 (d) 18
  32. 32.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 30 (c) 39 (d) 40
  33. 33.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
  34. 34.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 15 (b) 5 (c) 16 (d) 17
  36. 36.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 212 (b) 201 (c) 211 (d) 210
  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 42? (a) 5 (b) 4 (c) 7 (d) 8
  39. 39.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) 6 (b) 18 (c) 54 (d) 21
  40. 40.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 634 (c) 494 (d) 633

Answer key

  1. 594
  2. 61
  3. 555
  4. 19
  5. 3
  6. 4
  7. 195
  8. 6
  9. 5
  10. 321
  11. 5
  12. 21
  13. 60
  14. 17
  15. 4
  16. 63
  17. 552
  18. 14
  19. 14
  20. 155
  21. 4
  22. 20
  23. 2
  24. 17
  25. 15
  26. 17
  27. 69
  28. 5
  29. 165
  30. 18
  31. 17
  32. 39
  33. 36
  34. 7
  35. 16
  36. 210
  37. 3
  38. 7
  39. 18
  40. 633

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