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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 982 · 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 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 50 (c) 42 (d) 41
  2. 2.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) 30 (b) 10 (c) 33 (d) 90
  3. 3.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 82 (c) 81 (d) 72
  4. 4.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) 216 (b) 72 (c) 75 (d) 24
  5. 5.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  6. 6.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 8 (d) 10
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 86? (a) 7 (b) 8 (c) 9 (d) 6
  8. 8.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 276 (c) 286 (d) 262
  9. 9.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 261 (c) 252 (d) 246
  10. 10.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 5 (b) 15 (c) 16 (d) 17
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 40? (a) 3 (b) 2 (c) 4 (d) 5
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 12 (b) 14 (c) 3 (d) 13
  14. 14.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 63 (b) 72 (c) 64 (d) 54
  15. 15.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) 21 (c) 18 (d) 54
  16. 16.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 134 (c) 152 (d) 143
  17. 17.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) 189 (b) 66 (c) 63 (d) 21
  18. 18.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) 24 (c) 7 (d) 21
  19. 19.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 19 (c) 60 (d) 57
  20. 20.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 4 (d) 6
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 65? (a) 13 (b) 10 (c) 6 (d) 12
  22. 22.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) 108 (b) 12 (c) 39 (d) 36
  23. 23.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) 59 (c) 50 (d) 60
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 3 (b) 8 (c) 9 (d) 10
  25. 25.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 220 (c) 219 (d) 218
  26. 26.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 378 (c) 387 (d) 330
  27. 27.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 16 (b) 18 (c) 17 (d) 6
  29. 29.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 61 (b) 62 (c) 52 (d) 70
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 68? (a) 7 (b) 5 (c) 6 (d) 4
  31. 31.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 211 (b) 201 (c) 212 (d) 210
  32. 32.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 213 (c) 222 (d) 223
  33. 33.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 13 (d) 8
  34. 34.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  35. 35.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
  36. 36.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) 13 (c) 117 (d) 42
  37. 37.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 5 (b) 7 (c) 6 (d) 8
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 76? (a) 18 (b) 19 (c) 17 (d) 7
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 46? (a) 4 (b) 13 (c) 12 (d) 11

Answer key

  1. 41
  2. 30
  3. 81
  4. 72
  5. 5
  6. 9
  7. 8
  8. 285
  9. 261
  10. 2
  11. 16
  12. 4
  13. 13
  14. 63
  15. 18
  16. 143
  17. 63
  18. 21
  19. 57
  20. 5
  21. 12
  22. 36
  23. 59
  24. 9
  25. 219
  26. 387
  27. 9
  28. 17
  29. 61
  30. 6
  31. 210
  32. 222
  33. 7
  34. 8
  35. 2
  36. 39
  37. 3
  38. 7
  39. 18
  40. 12

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