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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 185 · 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) 2 (b) 4 (c) 3 (d) 10
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 7 (b) 18 (c) 17 (d) 16
  3. 3.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  4. 4.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) 39 (c) 42 (d) 117
  5. 5.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 168 (c) 167 (d) 158
  6. 6.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  7. 7.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 432 (c) 541 (d) 540
  8. 8.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  9. 9.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 504 (b) 495 (c) 505 (d) 408
  10. 10.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) 36 (c) 39 (d) 108
  11. 11.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 72 (c) 23 (d) 69
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 7 (b) 6 (c) 8 (d) 5
  14. 14.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 607 (c) 597 (d) 476
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 3 (b) 5 (c) 4 (d) 6
  16. 16.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 95? (a) 20 (b) 18 (c) 19 (d) 9
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 96? (a) 20 (b) 21 (c) 19 (d) 9
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 15 (b) 7 (c) 12 (d) 14
  20. 20.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 5 (d) 7
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 15 (d) 14
  22. 22.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 601 (c) 600 (d) 472
  23. 23.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4
  24. 24.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) 11 (b) 36 (c) 99 (d) 33
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 17 (b) 18 (c) 6 (d) 16
  26. 26.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) 171 (d) 19
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 12 (b) 11 (c) 3 (d) 13
  28. 28.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  29. 29.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 30 (b) 39 (c) 40 (d) 48
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 93? (a) 9 (b) 19 (c) 20 (d) 18
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 3 (b) 5 (c) 4 (d) 2
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 4 (b) 2 (c) 5 (d) 3
  33. 33.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) 18 (c) 162 (d) 57
  34. 34.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) 21 (d) 63
  35. 35.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) 24 (d) 75
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 5 (b) 3 (c) 4 (d) 2
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 12 (b) 14 (c) 3 (d) 13
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 19 (b) 7 (c) 17 (d) 18
  39. 39.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 148 (c) 140 (d) 139
  40. 40.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 166 (c) 157 (d) 148

Answer key

  1. 3
  2. 17
  3. 7
  4. 39
  5. 167
  6. 9
  7. 540
  8. 8
  9. 504
  10. 36
  11. 69
  12. 5
  13. 7
  14. 606
  15. 5
  16. 5
  17. 19
  18. 20
  19. 14
  20. 6
  21. 15
  22. 600
  23. 4
  24. 33
  25. 17
  26. 57
  27. 12
  28. 7
  29. 39
  30. 19
  31. 4
  32. 4
  33. 54
  34. 21
  35. 72
  36. 4
  37. 13
  38. 18
  39. 139
  40. 157

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