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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 876 · 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 2? (a) 10 (b) 1 (c) 2 (d) 3
  2. 2.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 99? (a) 9 (b) 20 (c) 21 (d) 19
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 91? (a) 9 (b) 11 (c) 10 (d) 12
  5. 5.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  6. 6.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 127 (b) 128 (c) 136 (d) 118
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 3 (b) 4 (c) 5 (d) 2
  8. 8.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) 69 (b) 72 (c) 23 (d) 207
  9. 9.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) 57 (b) 18 (c) 162 (d) 54
  10. 10.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 378 (c) 387 (d) 330
  11. 11.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 303 (c) 294 (d) 274
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 2 (b) 5 (c) 3 (d) 4
  13. 13.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) 42 (c) 13 (d) 117
  14. 14.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) 24 (b) 216 (c) 72 (d) 75
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 4 (b) 3 (c) 2 (d) 5
  16. 16.The numbers 13 to 21 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) 17 (c) 153 (d) 51
  17. 17.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 15 (d) 5
  18. 18.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
  19. 19.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 85 (b) 86 (c) 94 (d) 76
  20. 20.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
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 16 (b) 15 (c) 4 (d) 14
  22. 22.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 362 (b) 426 (c) 435 (d) 436
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 13 (b) 3 (c) 12 (d) 14
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 17 (b) 8 (c) 18 (d) 19
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 3 (b) 4 (c) 6 (d) 5
  26. 26.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) 144 (c) 16 (d) 51
  27. 27.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
  28. 28.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 5 (d) 7
  29. 29.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 8 (d) 11
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 2 (b) 3 (c) 5 (d) 4
  31. 31.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 8 (d) 13
  32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 63? (a) 5 (b) 4 (c) 6 (d) 7
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 72? (a) 10 (b) 11 (c) 7 (d) 8
  34. 34.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 198 (c) 69 (d) 22
  35. 35.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 107 (c) 108 (d) 116
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 13 (b) 15 (c) 3 (d) 14
  37. 37.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 609 (c) 619 (d) 618
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 3 (b) 6 (c) 5 (d) 4
  39. 39.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) 45 (b) 42 (c) 14 (d) 126
  40. 40.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) 33 (b) 10 (c) 90 (d) 30

Answer key

  1. 2
  2. 2
  3. 20
  4. 11
  5. 3
  6. 127
  7. 4
  8. 69
  9. 54
  10. 387
  11. 303
  12. 4
  13. 39
  14. 72
  15. 4
  16. 51
  17. 5
  18. 3
  19. 85
  20. 36
  21. 15
  22. 435
  23. 13
  24. 18
  25. 5
  26. 48
  27. 16
  28. 6
  29. 9
  30. 4
  31. 7
  32. 6
  33. 10
  34. 66
  35. 107
  36. 14
  37. 618
  38. 5
  39. 42
  40. 30

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