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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 426 · 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 two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  2. 2.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) 21 (d) 66
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 4 (b) 14 (c) 13 (d) 15
  4. 4.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 474 (c) 483 (d) 484
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 5 (b) 3 (c) 4 (d) 2
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 5 (b) 6 (c) 4 (d) 3
  7. 7.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 517 (b) 416 (c) 516 (d) 507
  8. 8.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) 108 (d) 12
  9. 9.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
  10. 10.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) 57 (b) 162 (c) 18 (d) 54
  11. 11.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 258 (c) 250 (d) 267
  12. 12.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) 36 (c) 99 (d) 33
  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) 51 (b) 54 (c) 17 (d) 153
  14. 14.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 472 (c) 600 (d) 601
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 54? (a) 15 (b) 17 (c) 5 (d) 16
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 17 (b) 16 (c) 15 (d) 5
  17. 17.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  18. 18.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) 13 (b) 117 (c) 42 (d) 39
  19. 19.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 259 (b) 244 (c) 249 (d) 258
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 17 (b) 16 (c) 6 (d) 18
  21. 21.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
  22. 22.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) 21 (b) 63 (c) 24 (d) 7
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 14 (b) 4 (c) 15 (d) 16
  24. 24.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 148 (c) 158 (d) 157
  25. 25.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) 8 (c) 72 (d) 27
  26. 26.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 397 (b) 387 (c) 396 (d) 336
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 57? (a) 6 (b) 5 (c) 4 (d) 3
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 6 (b) 16 (c) 17 (d) 18
  29. 29.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
  30. 30.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  31. 31.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 90 (c) 99 (d) 108
  32. 32.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 55 (b) 64 (c) 46 (d) 56
  33. 33.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 49 (b) 58 (c) 50 (d) 40
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 20 (b) 9 (c) 21 (d) 19
  35. 35.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) 30 (b) 9 (c) 27 (d) 81
  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) 15 (b) 5 (c) 45 (d) 18
  37. 37.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
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 99? (a) 21 (b) 19 (c) 20 (d) 9
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 71? (a) 7 (b) 8 (c) 6 (d) 5
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 3 (b) 5 (c) 4 (d) 2

Answer key

  1. 5
  2. 63
  3. 14
  4. 483
  5. 4
  6. 5
  7. 516
  8. 36
  9. 69
  10. 54
  11. 267
  12. 33
  13. 51
  14. 600
  15. 16
  16. 16
  17. 4
  18. 39
  19. 258
  20. 17
  21. 3
  22. 21
  23. 15
  24. 157
  25. 24
  26. 396
  27. 5
  28. 17
  29. 9
  30. 2
  31. 99
  32. 55
  33. 49
  34. 20
  35. 27
  36. 15
  37. 45
  38. 20
  39. 7
  40. 4

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