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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 723 · 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.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 122 (c) 114 (d) 113
  2. 2.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 607 (b) 606 (c) 476 (d) 597
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 6 (b) 7 (c) 8 (d) 5
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 5 (b) 6 (c) 7 (d) 4
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
  6. 6.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 376 (c) 447 (d) 457
  7. 7.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 170 (c) 169 (d) 178
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 63? (a) 4 (b) 6 (c) 5 (d) 7
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 5 (b) 16 (c) 15 (d) 17
  10. 10.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
  11. 11.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
  12. 12.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) 7 (c) 63 (d) 24
  13. 13.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 9 (b) 20 (c) 19 (d) 21
  15. 15.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 42 (c) 41 (d) 32
  16. 16.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) 5 (b) 15 (c) 45 (d) 18
  17. 17.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) 72 (c) 216 (d) 24
  18. 18.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 21 (b) 19 (c) 20 (d) 9
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 6 (b) 3 (c) 5 (d) 4
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 72? (a) 8 (b) 11 (c) 7 (d) 10
  22. 22.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) 18 (c) 54 (d) 162
  23. 23.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 366 (c) 322 (d) 375
  24. 24.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 8 (d) 7
  25. 25.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 137 (c) 146 (d) 138
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 17 (b) 19 (c) 18 (d) 7
  27. 27.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 285 (c) 286 (d) 276
  28. 28.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 4 (b) 14 (c) 15 (d) 16
  30. 30.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 230 (b) 228 (c) 237 (d) 238
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 4 (b) 3 (c) 1 (d) 2
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 15 (b) 6 (c) 17 (d) 16
  33. 33.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 63 (c) 20 (d) 60
  34. 34.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 174 (c) 165 (d) 166
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 64? (a) 6 (b) 17 (c) 16 (d) 18
  36. 36.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) 81 (b) 30 (c) 27 (d) 9
  37. 37.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 16 (b) 8 (c) 15 (d) 13
  39. 39.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 598 (b) 470 (c) 588 (d) 597
  40. 40.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) 153 (b) 51 (c) 54 (d) 17

Answer key

  1. 113
  2. 606
  3. 7
  4. 6
  5. 6
  6. 456
  7. 169
  8. 6
  9. 16
  10. 9
  11. 2
  12. 21
  13. 7
  14. 20
  15. 41
  16. 15
  17. 72
  18. 8
  19. 20
  20. 5
  21. 10
  22. 54
  23. 375
  24. 8
  25. 137
  26. 18
  27. 285
  28. 5
  29. 15
  30. 237
  31. 3
  32. 16
  33. 60
  34. 165
  35. 17
  36. 27
  37. 5
  38. 15
  39. 597
  40. 51

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