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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 212 · 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 times is the digit 4 written when you write all the numbers from 1 to 71? (a) 18 (b) 7 (c) 16 (d) 17
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 50? (a) 4 (b) 3 (c) 6 (d) 5
  3. 3.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  4. 4.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 11 (d) 8
  5. 5.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 8 (d) 13
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 79? (a) 7 (b) 17 (c) 19 (d) 18
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 6 (b) 16 (c) 17 (d) 18
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 93? (a) 19 (b) 18 (c) 20 (d) 9
  10. 10.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  11. 11.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 403 (c) 340 (d) 402
  12. 12.The numbers 12 to 20 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) 51 (c) 144 (d) 16
  13. 13.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  14. 14.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
  15. 15.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 139 (b) 148 (c) 130 (d) 140
  16. 16.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) 54 (b) 18 (c) 57 (d) 162
  17. 17.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 366 (c) 441 (d) 442
  18. 18.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 5 (d) 16
  19. 19.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) 81 (b) 9 (c) 30 (d) 27
  20. 20.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 82 (c) 64 (d) 73
  21. 21.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 472 (c) 600 (d) 601
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
  23. 23.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 159 (c) 150 (d) 168
  24. 24.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 164 (c) 155 (d) 146
  25. 25.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 11 (d) 8
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 8 (b) 17 (c) 18 (d) 19
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 46? (a) 4 (b) 12 (c) 11 (d) 13
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 8 (b) 20 (c) 19 (d) 18
  29. 29.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
  30. 30.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) 21 (b) 66 (c) 63 (d) 189
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 18 (d) 7
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 74? (a) 19 (b) 18 (c) 7 (d) 17
  33. 33.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 87 (b) 96 (c) 88 (d) 78
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 20 (b) 9 (c) 19 (d) 21
  35. 35.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) 223 (d) 222
  36. 36.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 213 (b) 204 (c) 321 (d) 214
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 95? (a) 18 (b) 19 (c) 9 (d) 20
  38. 38.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) 15 (b) 48 (c) 45 (d) 135
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 56? (a) 15 (b) 17 (c) 16 (d) 5
  40. 40.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 14 (c) 42 (d) 45

Answer key

  1. 17
  2. 5
  3. 2
  4. 9
  5. 7
  6. 18
  7. 17
  8. 5
  9. 19
  10. 8
  11. 402
  12. 48
  13. 6
  14. 5
  15. 139
  16. 54
  17. 441
  18. 4
  19. 27
  20. 73
  21. 600
  22. 2
  23. 159
  24. 155
  25. 9
  26. 18
  27. 12
  28. 19
  29. 8
  30. 63
  31. 18
  32. 18
  33. 87
  34. 20
  35. 222
  36. 213
  37. 19
  38. 45
  39. 16
  40. 42

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