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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 731 · 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 8 written when you write all the numbers from 1 to 97? (a) 18 (b) 9 (c) 19 (d) 20
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 18 (b) 6 (c) 17 (d) 16
  3. 3.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) 30 (c) 90 (d) 10
  4. 4.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  5. 5.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) 23 (c) 72 (d) 69
  6. 6.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
  7. 7.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 306 (c) 282 (d) 315
  8. 8.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  9. 9.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 37 (c) 46 (d) 28
  10. 10.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) 21 (c) 18 (d) 6
  11. 11.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 391 (c) 381 (d) 332
  12. 12.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) 27 (b) 8 (c) 72 (d) 24
  13. 13.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) 135 (b) 15 (c) 48 (d) 45
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 4 (b) 2 (c) 1 (d) 3
  15. 15.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  16. 16.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7
  17. 17.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 7 (d) 6
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 3 (b) 2 (c) 1 (d) 4
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 7 (b) 9 (c) 10 (d) 5
  20. 20.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 141 (c) 132 (d) 142
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 16 (b) 17 (c) 18 (d) 6
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 9 (b) 21 (c) 20 (d) 19
  23. 23.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) 292 (d) 321
  24. 24.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) 108 (b) 12 (c) 36 (d) 39
  25. 25.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 198 (c) 208 (d) 210
  26. 26.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) 51 (b) 153 (c) 17 (d) 54
  27. 27.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  28. 28.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 19 (b) 21 (c) 9 (d) 20
  30. 30.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) 36 (b) 99 (c) 11 (d) 33
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 14 (b) 3 (c) 13 (d) 15
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 68? (a) 16 (b) 18 (c) 17 (d) 6
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 4 (b) 5 (c) 6 (d) 3
  34. 34.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) 42 (d) 117
  35. 35.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 118 (c) 136 (d) 127
  36. 36.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 6 (d) 15
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 7 (b) 16 (c) 17 (d) 18
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 8 (b) 19 (c) 20 (d) 18
  39. 39.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 205 (c) 208 (d) 204
  40. 40.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 396 (c) 487 (d) 486

Answer key

  1. 19
  2. 17
  3. 30
  4. 3
  5. 69
  6. 4
  7. 315
  8. 6
  9. 37
  10. 18
  11. 390
  12. 24
  13. 45
  14. 3
  15. 7
  16. 6
  17. 7
  18. 3
  19. 9
  20. 141
  21. 17
  22. 20
  23. 330
  24. 36
  25. 207
  26. 51
  27. 5
  28. 9
  29. 20
  30. 33
  31. 14
  32. 17
  33. 5
  34. 39
  35. 127
  36. 5
  37. 17
  38. 19
  39. 204
  40. 486

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