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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 190 · 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 6 written when you write all the numbers from 1 to 94? (a) 20 (b) 19 (c) 9 (d) 18
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 5 (b) 8 (c) 7 (d) 6
  3. 3.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) 207 (c) 23 (d) 72
  4. 4.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 459 (c) 460 (d) 378
  5. 5.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 348 (c) 415 (d) 414
  6. 6.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  7. 7.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  8. 8.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) 216 (c) 24 (d) 72
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 2 (b) 4 (c) 1 (d) 3
  10. 10.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 198 (c) 208 (d) 207
  11. 11.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 4 (d) 2
  12. 12.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) 48 (b) 15 (c) 135 (d) 45
  13. 13.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) 60 (b) 19 (c) 171 (d) 57
  14. 14.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) 36 (c) 39 (d) 12
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 4 (b) 5 (c) 3 (d) 6
  16. 16.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  17. 17.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 167 (b) 176 (c) 168 (d) 158
  18. 18.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 319 (b) 318 (c) 309 (d) 284
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 13 (b) 3 (c) 15 (d) 14
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 13 (b) 14 (c) 3 (d) 15
  21. 21.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) 51 (b) 48 (c) 144 (d) 16
  22. 22.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 9 (d) 11
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 18 (b) 17 (c) 6 (d) 16
  24. 24.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) 81 (c) 27 (d) 30
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 16 (b) 6 (c) 18 (d) 17
  26. 26.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 349 (c) 339 (d) 304
  27. 27.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
  28. 28.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 80? (a) 9 (b) 8 (c) 7 (d) 10
  30. 30.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) 162 (c) 18 (d) 57
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 16 (b) 14 (c) 4 (d) 15
  32. 32.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  33. 33.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) 117 (c) 13 (d) 42
  34. 34.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) 18 (b) 54 (c) 21 (d) 6
  35. 35.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 115 (c) 124 (d) 106
  36. 36.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  37. 37.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 453 (b) 463 (c) 462 (d) 380
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 2 (b) 1 (c) 4 (d) 3
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 1 (b) 4 (c) 2 (d) 3
  40. 40.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) 99 (b) 11 (c) 33 (d) 36

Answer key

  1. 19
  2. 7
  3. 69
  4. 459
  5. 414
  6. 6
  7. 5
  8. 72
  9. 3
  10. 207
  11. 3
  12. 45
  13. 57
  14. 36
  15. 5
  16. 7
  17. 167
  18. 318
  19. 14
  20. 14
  21. 48
  22. 9
  23. 17
  24. 27
  25. 17
  26. 348
  27. 8
  28. 2
  29. 9
  30. 54
  31. 15
  32. 8
  33. 39
  34. 18
  35. 115
  36. 9
  37. 462
  38. 3
  39. 3
  40. 33

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