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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 421 · 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.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 36 (c) 11 (d) 33
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 17 (b) 6 (c) 18 (d) 16
  3. 3.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) 24 (c) 7 (d) 63
  4. 4.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 182 (c) 181 (d) 172
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 58? (a) 17 (b) 15 (c) 5 (d) 16
  6. 6.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
  7. 7.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
  9. 9.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 74 (c) 92 (d) 83
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 21 (b) 19 (c) 9 (d) 20
  11. 11.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 11 (d) 8
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 13 (b) 15 (c) 14 (d) 3
  13. 13.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
  14. 14.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 12 (b) 4 (c) 13 (d) 14
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 66? (a) 4 (b) 6 (c) 7 (d) 5
  17. 17.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  18. 18.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 16 (b) 14 (c) 15 (d) 4
  20. 20.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 10 (d) 2
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 14 (b) 16 (c) 15 (d) 4
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 58? (a) 5 (b) 15 (c) 17 (d) 16
  23. 23.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
  24. 24.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 195 (c) 186 (d) 202
  25. 25.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 226 (c) 231 (d) 232
  26. 26.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
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 19 (b) 21 (c) 20 (d) 9
  28. 28.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  29. 29.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 7 (d) 10
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 98? (a) 9 (b) 20 (c) 21 (d) 19
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 4 (b) 5 (c) 3 (d) 6
  32. 32.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 134 (c) 124 (d) 133
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 3 (b) 4 (c) 5 (d) 2
  34. 34.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 10 (d) 6
  35. 35.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 58 (c) 76 (d) 67
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 85? (a) 12 (b) 14 (c) 15 (d) 8
  37. 37.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 630 (b) 631 (c) 621 (d) 492
  38. 38.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 148 (c) 130 (d) 139
  39. 39.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 142 (c) 141 (d) 150
  40. 40.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) 16 (c) 48 (d) 51

Answer key

  1. 33
  2. 17
  3. 21
  4. 181
  5. 16
  6. 72
  7. 5
  8. 5
  9. 83
  10. 20
  11. 9
  12. 14
  13. 42
  14. 7
  15. 13
  16. 6
  17. 3
  18. 4
  19. 15
  20. 3
  21. 15
  22. 16
  23. 17
  24. 195
  25. 231
  26. 30
  27. 20
  28. 6
  29. 6
  30. 20
  31. 5
  32. 133
  33. 4
  34. 7
  35. 67
  36. 14
  37. 630
  38. 139
  39. 141
  40. 48

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