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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 769 · 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 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 438 (c) 447 (d) 370
  2. 2.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 35 (c) 26 (d) 44
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 8 (b) 20 (c) 18 (d) 19
  4. 4.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 3 (b) 5 (c) 2 (d) 4
  6. 6.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  7. 7.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) 69 (b) 66 (c) 198 (d) 22
  8. 8.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 15 (d) 5
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 68? (a) 5 (b) 6 (c) 4 (d) 7
  10. 10.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  11. 11.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  12. 12.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 123 (b) 114 (c) 132 (d) 124
  13. 13.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) 144 (b) 51 (c) 16 (d) 48
  14. 14.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 210 (c) 218 (d) 220
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 1 (b) 2 (c) 3 (d) 4
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 2 (b) 3 (c) 5 (d) 4
  17. 17.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  18. 18.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 487 (c) 477 (d) 396
  19. 19.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) 13 (b) 42 (c) 39 (d) 117
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 13 (b) 15 (c) 3 (d) 14
  21. 21.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 16 (b) 18 (c) 17 (d) 6
  23. 23.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) 54 (c) 21 (d) 18
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 7 (b) 5 (c) 6 (d) 4
  25. 25.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) 72 (c) 24 (d) 216
  26. 26.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 456 (c) 466 (d) 382
  27. 27.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 3 (b) 2 (c) 4 (d) 1
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 4 (b) 16 (c) 14 (d) 15
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 89? (a) 19 (b) 18 (c) 8 (d) 20
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 6 (b) 18 (c) 16 (d) 17
  32. 32.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 238 (b) 249 (c) 250 (d) 240
  33. 33.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) 24 (b) 21 (c) 63 (d) 7
  34. 34.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) 51 (b) 17 (c) 153 (d) 54
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 7 (b) 8 (c) 5 (d) 6
  36. 36.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) 20 (c) 63 (d) 60
  37. 37.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 174 (c) 192 (d) 183
  38. 38.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 243 (c) 351 (d) 244
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 20 (b) 19 (c) 18 (d) 9
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 99? (a) 21 (b) 9 (c) 20 (d) 19

Answer key

  1. 447
  2. 35
  3. 19
  4. 3
  5. 4
  6. 7
  7. 66
  8. 5
  9. 6
  10. 6
  11. 8
  12. 123
  13. 48
  14. 219
  15. 3
  16. 4
  17. 2
  18. 486
  19. 39
  20. 14
  21. 6
  22. 17
  23. 18
  24. 6
  25. 72
  26. 465
  27. 9
  28. 3
  29. 15
  30. 19
  31. 17
  32. 249
  33. 21
  34. 51
  35. 7
  36. 60
  37. 183
  38. 243
  39. 19
  40. 20

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