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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 895 · 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 3 written when you write all the numbers from 1 to 50? (a) 16 (b) 15 (c) 14 (d) 5
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 84? (a) 19 (b) 18 (c) 8 (d) 17
  3. 3.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) 9 (b) 30 (c) 27 (d) 81
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 9 (b) 19 (c) 20 (d) 21
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 5 (b) 3 (c) 4 (d) 2
  6. 6.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
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 3 (b) 7 (c) 4 (d) 6
  8. 8.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
  9. 9.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) 14 (c) 126 (d) 42
  10. 10.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
  11. 11.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 331 (c) 330 (d) 292
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 2 (b) 4 (c) 1 (d) 3
  13. 13.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) 17 (b) 51 (c) 54 (d) 153
  14. 14.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 70 (c) 69 (d) 78
  15. 15.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
  16. 16.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 99? (a) 9 (b) 19 (c) 21 (d) 20
  18. 18.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) 27 (c) 72 (d) 8
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 3 (b) 2 (c) 4 (d) 5
  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) 36 (b) 39 (c) 12 (d) 108
  21. 21.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 170 (c) 161 (d) 162
  22. 22.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 8 (d) 11
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 1 (d) 4
  24. 24.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) 6 (b) 21 (c) 54 (d) 18
  25. 25.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 20 (b) 18 (c) 19 (d) 8
  27. 27.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 553 (c) 440 (d) 552
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 21 (b) 19 (c) 9 (d) 20
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 15 (b) 16 (c) 5 (d) 17
  30. 30.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  31. 31.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) 18 (b) 162 (c) 54 (d) 57
  32. 32.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 147 (b) 156 (c) 138 (d) 148
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 58? (a) 15 (b) 17 (c) 5 (d) 16
  34. 34.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 368 (c) 444 (d) 445
  35. 35.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 104 (c) 86 (d) 95
  36. 36.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) 5 (d) 45
  37. 37.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 342 (c) 306 (d) 352
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 8 (b) 19 (c) 18 (d) 20
  39. 39.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 540 (c) 541 (d) 531
  40. 40.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

Answer key

  1. 15
  2. 18
  3. 27
  4. 20
  5. 4
  6. 39
  7. 6
  8. 48
  9. 42
  10. 69
  11. 330
  12. 3
  13. 51
  14. 69
  15. 6
  16. 9
  17. 20
  18. 24
  19. 4
  20. 36
  21. 161
  22. 9
  23. 3
  24. 18
  25. 3
  26. 19
  27. 552
  28. 20
  29. 16
  30. 6
  31. 54
  32. 147
  33. 16
  34. 444
  35. 95
  36. 15
  37. 351
  38. 19
  39. 540
  40. 139

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