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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 162 · 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.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) 18 (d) 45
  2. 2.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 248 (b) 255 (c) 264 (d) 265
  3. 3.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 630 (c) 631 (d) 492
  4. 4.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) 81 (c) 9 (d) 27
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 57? (a) 6 (b) 5 (c) 3 (d) 4
  6. 6.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 238 (c) 250 (d) 249
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  8. 8.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) 48 (c) 45 (d) 135
  9. 9.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 447 (c) 438 (d) 448
  10. 10.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) 51 (b) 144 (c) 16 (d) 48
  11. 11.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  12. 12.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) 63 (b) 180 (c) 20 (d) 60
  13. 13.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) 90 (b) 10 (c) 33 (d) 30
  14. 14.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
  15. 15.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) 24 (b) 21 (c) 63 (d) 7
  16. 16.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 60 (c) 69 (d) 78
  17. 17.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) 108 (c) 12 (d) 39
  18. 18.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 44 (c) 53 (d) 62
  19. 19.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) 162 (d) 54
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 21 (b) 19 (c) 9 (d) 20
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 97? (a) 19 (b) 18 (c) 9 (d) 20
  22. 22.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 499 (c) 498 (d) 404
  23. 23.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 528 (c) 538 (d) 537
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 15 (b) 13 (c) 3 (d) 14
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 4 (b) 7 (c) 5 (d) 6
  26. 26.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  27. 27.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 405 (c) 396 (d) 342
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 17 (b) 19 (c) 7 (d) 18
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 18 (b) 7 (c) 16 (d) 17
  30. 30.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) 450 (c) 568 (d) 558
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 18 (b) 16 (c) 17 (d) 6
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 88? (a) 19 (b) 17 (c) 8 (d) 18
  33. 33.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) 19 (b) 171 (c) 57 (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) 166 (b) 156 (c) 165 (d) 174
  35. 35.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) 117 (b) 13 (c) 39 (d) 42
  36. 36.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) 45 (d) 126
  37. 37.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 6 (b) 18 (c) 17 (d) 16
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 70? (a) 9 (b) 7 (c) 6 (d) 8
  40. 40.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 613 (c) 480 (d) 603

Answer key

  1. 15
  2. 264
  3. 630
  4. 27
  5. 5
  6. 249
  7. 4
  8. 45
  9. 447
  10. 48
  11. 5
  12. 60
  13. 30
  14. 72
  15. 21
  16. 69
  17. 36
  18. 53
  19. 54
  20. 20
  21. 19
  22. 498
  23. 537
  24. 14
  25. 6
  26. 3
  27. 405
  28. 18
  29. 17
  30. 567
  31. 17
  32. 18
  33. 57
  34. 165
  35. 39
  36. 42
  37. 8
  38. 17
  39. 8
  40. 612

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