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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 693 · 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 2 written when you write all the numbers from 1 to 31? (a) 13 (b) 12 (c) 3 (d) 14
  2. 2.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  3. 3.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) 83 (c) 92 (d) 74
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 12 (b) 7 (c) 14 (d) 15
  5. 5.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
  6. 6.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) 7 (c) 63 (d) 21
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 6 (b) 17 (c) 18 (d) 16
  8. 8.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) 33 (b) 99 (c) 11 (d) 36
  9. 9.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 291 (c) 272 (d) 301
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 80? (a) 17 (b) 8 (c) 19 (d) 18
  11. 11.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
  12. 12.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 331 (c) 321 (d) 292
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 17 (b) 8 (c) 18 (d) 19
  14. 14.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) 42 (b) 126 (c) 45 (d) 14
  15. 15.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) 39 (b) 12 (c) 108 (d) 36
  16. 16.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) 20 (b) 60 (c) 63 (d) 180
  17. 17.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 205 (c) 204 (d) 195
  18. 18.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 322 (c) 321 (d) 312
  19. 19.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 177 (c) 186 (d) 178
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 17 (b) 19 (c) 18 (d) 7
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 7 (b) 17 (c) 16 (d) 18
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 67? (a) 15 (b) 14 (c) 6 (d) 16
  23. 23.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 15 (d) 6
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 20 (b) 9 (c) 19 (d) 18
  25. 25.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) 33 (d) 30
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 19 (b) 18 (c) 17 (d) 8
  27. 27.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 52 (c) 34 (d) 43
  28. 28.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 16 (d) 3
  29. 29.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 3 (d) 17
  30. 30.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) 39 (b) 13 (c) 117 (d) 42
  31. 31.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  32. 32.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 100 (c) 91 (d) 82
  33. 33.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) 216 (b) 72 (c) 75 (d) 24
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 14 (b) 15 (c) 3 (d) 13
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 15 (b) 16 (c) 5 (d) 17
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 21 (b) 9 (c) 20 (d) 19
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 1 (b) 3 (c) 4 (d) 2
  38. 38.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 19 (b) 18 (c) 7 (d) 17
  40. 40.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) 54 (b) 6 (c) 18 (d) 21

Answer key

  1. 13
  2. 3
  3. 83
  4. 14
  5. 2
  6. 21
  7. 17
  8. 33
  9. 300
  10. 18
  11. 48
  12. 330
  13. 18
  14. 42
  15. 36
  16. 60
  17. 204
  18. 321
  19. 177
  20. 18
  21. 17
  22. 15
  23. 5
  24. 19
  25. 30
  26. 18
  27. 43
  28. 4
  29. 3
  30. 39
  31. 9
  32. 91
  33. 72
  34. 14
  35. 16
  36. 20
  37. 3
  38. 5
  39. 18
  40. 18

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