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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 786 · 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 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 171 (c) 162 (d) 180
  2. 2.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 122 (c) 132 (d) 131
  3. 3.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 3 (b) 2 (c) 5 (d) 4
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 2 (b) 4 (c) 5 (d) 3
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 7 (b) 9 (c) 6 (d) 8
  7. 7.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 171 (c) 57 (d) 19
  8. 8.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 12 (d) 9
  9. 9.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 631 (b) 621 (c) 492 (d) 630
  10. 10.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) 21 (b) 18 (c) 6 (d) 54
  11. 11.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11
  12. 12.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
  13. 13.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 278 (b) 309 (c) 310 (d) 300
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 65? (a) 6 (b) 18 (c) 17 (d) 16
  15. 15.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 18 (b) 7 (c) 17 (d) 19
  17. 17.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) 36 (b) 33 (c) 99 (d) 11
  18. 18.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 238 (c) 237 (d) 230
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 16 (b) 15 (c) 13 (d) 8
  20. 20.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
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 1 (b) 3 (c) 2 (d) 4
  22. 22.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) 9 (d) 81
  23. 23.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 402 (c) 340 (d) 403
  24. 24.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 4 (d) 6
  25. 25.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 432 (c) 441 (d) 442
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 19 (b) 18 (c) 20 (d) 8
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 14 (b) 5 (c) 16 (d) 15
  28. 28.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 421 (b) 352 (c) 420 (d) 411
  29. 29.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) 216 (d) 24
  30. 30.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 8 (b) 9 (c) 7 (d) 6
  32. 32.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 99? (a) 20 (b) 21 (c) 9 (d) 19
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 21 (b) 9 (c) 19 (d) 20
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 56? (a) 15 (b) 16 (c) 5 (d) 17
  36. 36.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 452 (b) 561 (c) 570 (d) 571
  37. 37.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) 72 (b) 207 (c) 69 (d) 23
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 14 (b) 16 (c) 15 (d) 4
  39. 39.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 378 (c) 450 (d) 459
  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) 54 (b) 51 (c) 17 (d) 153

Answer key

  1. 171
  2. 131
  3. 6
  4. 4
  5. 4
  6. 8
  7. 57
  8. 8
  9. 630
  10. 18
  11. 9
  12. 9
  13. 309
  14. 17
  15. 7
  16. 18
  17. 33
  18. 237
  19. 15
  20. 21
  21. 3
  22. 27
  23. 402
  24. 5
  25. 441
  26. 19
  27. 15
  28. 420
  29. 72
  30. 5
  31. 8
  32. 7
  33. 20
  34. 20
  35. 16
  36. 570
  37. 69
  38. 15
  39. 459
  40. 51

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