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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 875 · 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 two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 19 (b) 8 (c) 20 (d) 18
  3. 3.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 9 (b) 21 (c) 19 (d) 20
  5. 5.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) 18 (b) 45 (c) 5 (d) 15
  6. 6.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) 21 (d) 63
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 9 (b) 6 (c) 7 (d) 8
  8. 8.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 8 (d) 6
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 9 (b) 11 (c) 6 (d) 12
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 19 (b) 21 (c) 9 (d) 20
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 3 (b) 14 (c) 12 (d) 13
  12. 12.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
  13. 13.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 47 (c) 56 (d) 38
  14. 14.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 254 (c) 274 (d) 264
  15. 15.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 72 (c) 24 (d) 27
  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) 19 (b) 60 (c) 171 (d) 57
  17. 17.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
  18. 18.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 70 (c) 61 (d) 62
  19. 19.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) 18 (b) 6 (c) 21 (d) 54
  20. 20.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 185 (b) 194 (c) 186 (d) 176
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 12 (b) 13 (c) 14 (d) 4
  22. 22.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) 90 (b) 10 (c) 30 (d) 33
  23. 23.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 54 (c) 46 (d) 45
  24. 24.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 630 (b) 640 (c) 639 (d) 498
  25. 25.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 10 (d) 7
  26. 26.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) 21 (b) 63 (c) 7 (d) 24
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 70? (a) 18 (b) 17 (c) 16 (d) 7
  28. 28.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 93 (c) 84 (d) 94
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 65? (a) 5 (b) 4 (c) 6 (d) 7
  30. 30.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 99? (a) 9 (b) 19 (c) 21 (d) 20
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 7 (b) 4 (c) 6 (d) 5
  33. 33.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) 45 (b) 15 (c) 48 (d) 135
  34. 34.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  35. 35.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
  36. 36.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) 57 (c) 18 (d) 162
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 80? (a) 18 (b) 8 (c) 17 (d) 19
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 15 (b) 17 (c) 6 (d) 16
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 16 (b) 6 (c) 17 (d) 18
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 20 (b) 19 (c) 18 (d) 9

Answer key

  1. 3
  2. 19
  3. 6
  4. 20
  5. 15
  6. 63
  7. 8
  8. 7
  9. 11
  10. 20
  11. 13
  12. 8
  13. 47
  14. 273
  15. 24
  16. 57
  17. 4
  18. 61
  19. 18
  20. 185
  21. 13
  22. 30
  23. 45
  24. 639
  25. 6
  26. 21
  27. 17
  28. 93
  29. 6
  30. 5
  31. 20
  32. 6
  33. 45
  34. 8
  35. 9
  36. 54
  37. 18
  38. 16
  39. 17
  40. 19

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