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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 280 · 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 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 210 (c) 219 (d) 218
  2. 2.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  3. 3.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 567 (c) 577 (d) 456
  4. 4.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
  5. 5.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) 24 (b) 75 (c) 216 (d) 72
  6. 6.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  8. 8.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) 30 (b) 33 (c) 10 (d) 90
  9. 9.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 9 (d) 7
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 54? (a) 5 (b) 17 (c) 15 (d) 16
  11. 11.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 232 (c) 231 (d) 226
  12. 12.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) 18 (c) 57 (d) 162
  13. 13.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 5 (b) 4 (c) 3 (d) 6
  15. 15.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 384 (c) 375 (d) 385
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 18 (b) 16 (c) 17 (d) 6
  17. 17.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 10 (d) 11
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 15 (b) 4 (c) 16 (d) 14
  19. 19.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
  20. 20.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  21. 21.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 217 (b) 216 (c) 207 (d) 324
  22. 22.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 403 (b) 393 (c) 402 (d) 340
  23. 23.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 198 (b) 69 (c) 66 (d) 22
  24. 24.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 4 (d) 6
  25. 25.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) 144 (b) 16 (c) 51 (d) 48
  26. 26.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  27. 27.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 568 (c) 558 (d) 450
  28. 28.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) 8 (b) 24 (c) 27 (d) 72
  29. 29.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 294 (c) 304 (d) 303
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 20 (d) 19
  31. 31.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 83 (b) 92 (c) 84 (d) 74
  32. 32.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 42 (c) 51 (d) 52
  33. 33.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) 27 (b) 30 (c) 81 (d) 9
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 4 (b) 1 (c) 3 (d) 2
  35. 35.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  36. 36.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) 11 (c) 99 (d) 36
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 7 (b) 18 (c) 19 (d) 17
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 19 (d) 21
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 85? (a) 8 (b) 9 (c) 7 (d) 6
  40. 40.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10

Answer key

  1. 219
  2. 6
  3. 576
  4. 2
  5. 72
  6. 5
  7. 2
  8. 30
  9. 8
  10. 16
  11. 231
  12. 54
  13. 8
  14. 5
  15. 384
  16. 17
  17. 9
  18. 15
  19. 4
  20. 6
  21. 216
  22. 402
  23. 66
  24. 5
  25. 48
  26. 3
  27. 567
  28. 24
  29. 303
  30. 19
  31. 83
  32. 51
  33. 27
  34. 3
  35. 7
  36. 33
  37. 18
  38. 20
  39. 8
  40. 3

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