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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 607 · 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.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 189 (b) 63 (c) 66 (d) 21
  2. 2.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) 42 (b) 13 (c) 117 (d) 39
  3. 3.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 249 (c) 259 (d) 258
  4. 4.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 374 (b) 453 (c) 444 (d) 454
  5. 5.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 7 (b) 19 (c) 17 (d) 18
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 7 (b) 17 (c) 19 (d) 18
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 80? (a) 8 (b) 9 (c) 6 (d) 7
  9. 9.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 83? (a) 19 (b) 20 (c) 8 (d) 18
  11. 11.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 7 (d) 14
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 5 (b) 3 (c) 2 (d) 4
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 3 (b) 11 (c) 9 (d) 10
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 2 (b) 3 (c) 4 (d) 5
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 8 (b) 3 (c) 9 (d) 10
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 77? (a) 18 (b) 17 (c) 7 (d) 19
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 75? (a) 19 (b) 7 (c) 18 (d) 17
  18. 18.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) 36 (d) 108
  19. 19.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
  20. 20.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) 15 (b) 45 (c) 5 (d) 18
  21. 21.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 499 (c) 498 (d) 404
  22. 22.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) 366 (c) 442 (d) 432
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 6 (b) 4 (c) 5 (d) 3
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 4 (b) 3 (c) 2 (d) 1
  25. 25.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) 23 (b) 72 (c) 207 (d) 69
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 76? (a) 5 (b) 8 (c) 7 (d) 6
  27. 27.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) 72 (b) 75 (c) 24 (d) 216
  28. 28.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) 16 (c) 144 (d) 48
  29. 29.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 300 (c) 301 (d) 272
  30. 30.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) 54 (c) 21 (d) 18
  31. 31.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
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 17 (b) 16 (c) 5 (d) 15
  33. 33.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  34. 34.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 28 (b) 46 (c) 37 (d) 38
  35. 35.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) 15 (b) 45 (c) 135 (d) 48
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 4 (b) 3 (c) 5 (d) 6
  37. 37.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 348 (c) 358 (d) 357
  38. 38.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 173 (b) 182 (c) 164 (d) 174
  39. 39.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 19 (b) 18 (c) 8 (d) 20

Answer key

  1. 63
  2. 39
  3. 258
  4. 453
  5. 4
  6. 18
  7. 18
  8. 8
  9. 9
  10. 19
  11. 6
  12. 4
  13. 10
  14. 4
  15. 9
  16. 18
  17. 18
  18. 36
  19. 8
  20. 15
  21. 498
  22. 441
  23. 5
  24. 3
  25. 69
  26. 7
  27. 72
  28. 48
  29. 300
  30. 18
  31. 42
  32. 16
  33. 2
  34. 37
  35. 45
  36. 5
  37. 357
  38. 173
  39. 4
  40. 19

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