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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 250 · 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 9 written when you write all the numbers from 1 to 94? (a) 15 (b) 14 (c) 12 (d) 9
  2. 2.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) 63 (c) 7 (d) 21
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 52? (a) 6 (b) 3 (c) 4 (d) 5
  4. 4.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 110 (c) 102 (d) 101
  5. 5.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) 16 (b) 144 (c) 51 (d) 48
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 3 (b) 2 (c) 1 (d) 4
  7. 7.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
  8. 8.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 2 (b) 4 (c) 1 (d) 3
  10. 10.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 144 (c) 126 (d) 135
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 58? (a) 6 (b) 5 (c) 7 (d) 4
  12. 12.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 139 (b) 148 (c) 140 (d) 130
  13. 13.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) 99 (c) 33 (d) 36
  14. 14.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
  15. 15.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  16. 16.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 261 (b) 270 (c) 271 (d) 252
  17. 17.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 132 (c) 123 (d) 124
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 75? (a) 19 (b) 17 (c) 7 (d) 18
  19. 19.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) 135 (d) 48
  20. 20.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
  21. 21.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) 24 (b) 72 (c) 27 (d) 8
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 21 (b) 9 (c) 19 (d) 20
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 85? (a) 18 (b) 8 (c) 20 (d) 19
  24. 24.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 4 (d) 3
  25. 25.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) 15 (c) 45 (d) 5
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 20 (b) 8 (c) 18 (d) 19
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 21 (b) 9 (c) 20 (d) 19
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 5 (d) 4
  29. 29.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
  30. 30.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) 57 (c) 60 (d) 171
  31. 31.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 382 (c) 456 (d) 465
  32. 32.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 9 (c) 30 (d) 81
  33. 33.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  34. 34.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 442 (c) 366 (d) 432
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 4 (b) 2 (c) 3 (d) 5
  36. 36.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 17 (b) 16 (c) 6 (d) 18
  38. 38.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
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 21 (b) 19 (c) 9 (d) 20
  40. 40.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 312 (c) 361 (d) 360

Answer key

  1. 14
  2. 21
  3. 5
  4. 101
  5. 48
  6. 3
  7. 72
  8. 2
  9. 3
  10. 135
  11. 6
  12. 139
  13. 33
  14. 6
  15. 3
  16. 270
  17. 123
  18. 18
  19. 45
  20. 8
  21. 24
  22. 20
  23. 19
  24. 4
  25. 15
  26. 19
  27. 20
  28. 5
  29. 7
  30. 57
  31. 465
  32. 27
  33. 4
  34. 441
  35. 4
  36. 9
  37. 17
  38. 36
  39. 20
  40. 360

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