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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 563 · 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 8 written when you write all the numbers from 1 to 43? (a) 4 (b) 3 (c) 5 (d) 2
  2. 2.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 11 (b) 3 (c) 13 (d) 12
  4. 4.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 577 (b) 576 (c) 567 (d) 456
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 4 (b) 16 (c) 15 (d) 14
  6. 6.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) 54 (b) 6 (c) 18 (d) 21
  7. 7.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 18 (b) 17 (c) 7 (d) 19
  9. 9.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 10 (b) 33 (c) 30 (d) 90
  10. 10.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) 42 (b) 14 (c) 126 (d) 45
  11. 11.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 138 (c) 128 (d) 137
  12. 12.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
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 9 (d) 10
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 19 (b) 18 (c) 20 (d) 8
  15. 15.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 235 (b) 225 (c) 234 (d) 228
  16. 16.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) 135 (c) 48 (d) 45
  17. 17.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  18. 18.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 50? (a) 6 (b) 3 (c) 4 (d) 5
  20. 20.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 253 (c) 240 (d) 243
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 4 (b) 16 (c) 14 (d) 15
  22. 22.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 259 (c) 244 (d) 258
  23. 23.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  24. 24.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 570 (c) 452 (d) 571
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 20 (b) 18 (c) 19 (d) 9
  26. 26.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) 42 (c) 39 (d) 117
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 16 (b) 15 (c) 4 (d) 14
  28. 28.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 10 (d) 11
  29. 29.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) 57 (c) 54 (d) 162
  30. 30.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) 33 (b) 36 (c) 11 (d) 99
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 9 (d) 20
  32. 32.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 8 (d) 11
  33. 33.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 487 (c) 477 (d) 396
  34. 34.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 174 (c) 192 (d) 183
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 20 (d) 9
  36. 36.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 15 (d) 5
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 46? (a) 4 (b) 3 (c) 2 (d) 5
  38. 38.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 376 (c) 322 (d) 375
  39. 39.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 622 (c) 612 (d) 621
  40. 40.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 351 (c) 361 (d) 360

Answer key

  1. 4
  2. 6
  3. 12
  4. 576
  5. 15
  6. 18
  7. 7
  8. 18
  9. 30
  10. 42
  11. 137
  12. 72
  13. 8
  14. 19
  15. 234
  16. 45
  17. 2
  18. 3
  19. 5
  20. 252
  21. 15
  22. 258
  23. 6
  24. 570
  25. 19
  26. 39
  27. 15
  28. 9
  29. 54
  30. 33
  31. 20
  32. 9
  33. 486
  34. 183
  35. 20
  36. 5
  37. 4
  38. 375
  39. 621
  40. 360

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