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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 992 · 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 7 written when you write all the numbers from 1 to 61? (a) 4 (b) 7 (c) 5 (d) 6
  2. 2.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 95? (a) 18 (b) 20 (c) 9 (d) 19
  4. 4.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) 546 (c) 556 (d) 555
  5. 5.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 613 (c) 480 (d) 612
  6. 6.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 490 (c) 628 (d) 627
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 20 (b) 8 (c) 18 (d) 19
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 17 (b) 19 (c) 18 (d) 7
  9. 9.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
  10. 10.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) 15 (b) 5 (c) 18 (d) 45
  11. 11.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  12. 12.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  13. 13.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 231 (c) 232 (d) 241
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 4 (b) 3 (c) 2 (d) 1
  15. 15.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) 72 (b) 216 (c) 24 (d) 75
  16. 16.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3
  17. 17.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 133 (c) 142 (d) 134
  18. 18.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  19. 19.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  20. 20.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  21. 21.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 5 (d) 4
  22. 22.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) 218 (c) 220 (d) 210
  23. 23.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 15 (b) 16 (c) 4 (d) 14
  25. 25.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 316 (c) 282 (d) 306
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 19 (b) 20 (c) 8 (d) 18
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 17 (b) 7 (c) 16 (d) 15
  28. 28.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
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 73? (a) 7 (b) 12 (c) 9 (d) 11
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 90? (a) 9 (b) 18 (c) 19 (d) 20
  31. 31.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 95 (b) 104 (c) 86 (d) 96
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 57? (a) 13 (b) 15 (c) 5 (d) 14
  33. 33.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) 10 (b) 30 (c) 33 (d) 90
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 7 (b) 18 (c) 17 (d) 19
  35. 35.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) 117 (d) 39
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 98? (a) 9 (b) 20 (c) 19 (d) 21
  37. 37.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
  38. 38.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 486 (c) 622 (d) 621
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 3 (b) 2 (c) 4 (d) 5
  40. 40.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 24 (c) 34 (d) 33

Answer key

  1. 6
  2. 4
  3. 19
  4. 555
  5. 612
  6. 627
  7. 19
  8. 18
  9. 17
  10. 15
  11. 3
  12. 2
  13. 240
  14. 3
  15. 72
  16. 2
  17. 133
  18. 6
  19. 9
  20. 3
  21. 4
  22. 219
  23. 7
  24. 15
  25. 315
  26. 19
  27. 16
  28. 54
  29. 11
  30. 19
  31. 95
  32. 14
  33. 30
  34. 18
  35. 39
  36. 20
  37. 9
  38. 621
  39. 4
  40. 33

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