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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 677 · 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 1 written when you write all the numbers from 1 to 73? (a) 17 (b) 18 (c) 7 (d) 19
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 92? (a) 20 (b) 19 (c) 9 (d) 18
  3. 3.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  4. 4.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 6 (b) 16 (c) 18 (d) 17
  6. 6.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 315 (c) 325 (d) 288
  7. 7.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  8. 8.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
  9. 9.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
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 21 (b) 20 (c) 19 (d) 9
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 95? (a) 9 (b) 19 (c) 20 (d) 18
  12. 12.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
  13. 13.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) 12 (b) 108 (c) 39 (d) 36
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 77? (a) 7 (b) 19 (c) 17 (d) 18
  15. 15.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 160 (c) 159 (d) 168
  16. 16.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) 57 (b) 60 (c) 19 (d) 171
  17. 17.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 56 (c) 55 (d) 64
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 5 (b) 13 (c) 14 (d) 12
  19. 19.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  20. 20.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) 14 (b) 45 (c) 126 (d) 42
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 6 (b) 7 (c) 8 (d) 5
  22. 22.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 3 (b) 14 (c) 15 (d) 13
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 8 (b) 6 (c) 7 (d) 5
  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) 216 (c) 72 (d) 24
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 17 (b) 19 (c) 18 (d) 8
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 18 (b) 6 (c) 16 (d) 17
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 16 (b) 4 (c) 15 (d) 14
  29. 29.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) 16 (d) 144
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 1 (d) 3
  31. 31.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 158 (c) 140 (d) 149
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 21 (b) 9 (c) 20 (d) 19
  33. 33.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) 41 (c) 42 (d) 50
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 8 (b) 19 (c) 18 (d) 20
  35. 35.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  36. 36.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 430 (c) 358 (d) 429
  37. 37.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 500 (c) 643 (d) 642
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 4 (b) 15 (c) 14 (d) 13
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 2 (b) 3 (c) 5 (d) 4
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 2 (b) 3 (c) 1 (d) 4

Answer key

  1. 18
  2. 19
  3. 2
  4. 3
  5. 17
  6. 324
  7. 6
  8. 8
  9. 60
  10. 20
  11. 19
  12. 4
  13. 36
  14. 18
  15. 159
  16. 57
  17. 55
  18. 13
  19. 8
  20. 42
  21. 7
  22. 9
  23. 14
  24. 7
  25. 72
  26. 18
  27. 17
  28. 15
  29. 48
  30. 3
  31. 149
  32. 20
  33. 41
  34. 19
  35. 2
  36. 429
  37. 642
  38. 14
  39. 4
  40. 3

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