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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 570 · 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 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) 24 (b) 8 (c) 27 (d) 72
  2. 2.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) 57 (c) 19 (d) 171
  3. 3.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 2 (d) 1
  4. 4.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) 63 (b) 21 (c) 7 (d) 24
  5. 5.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
  6. 6.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) 16 (b) 51 (c) 144 (d) 48
  7. 7.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 8 (d) 7
  8. 8.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 340 (b) 330 (c) 298 (d) 339
  9. 9.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 184 (c) 175 (d) 166
  10. 10.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 115 (b) 106 (c) 124 (d) 116
  11. 11.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) 48 (b) 15 (c) 135 (d) 45
  12. 12.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  13. 13.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) 27 (c) 81 (d) 9
  14. 14.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) 18 (c) 6 (d) 21
  15. 15.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 11 (d) 10
  16. 16.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 628 (b) 490 (c) 627 (d) 618
  17. 17.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 73 (b) 74 (c) 82 (d) 64
  18. 18.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) 60 (b) 20 (c) 63 (d) 180
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 4 (b) 2 (c) 5 (d) 3
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 16 (b) 6 (c) 18 (d) 17
  21. 21.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 9 (d) 10
  22. 22.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 567 (c) 568 (d) 558
  23. 23.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 2 (b) 3 (c) 4 (d) 5
  25. 25.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 399 (c) 409 (d) 344
  26. 26.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 355 (b) 308 (c) 354 (d) 345
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 18 (b) 8 (c) 17 (d) 19
  28. 28.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 4 (b) 3 (c) 1 (d) 2
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 16 (b) 4 (c) 15 (d) 14
  31. 31.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 573 (c) 583 (d) 582
  32. 32.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
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 6 (b) 5 (c) 4 (d) 3
  34. 34.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) 15 (b) 5 (c) 18 (d) 45
  35. 35.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 134 (c) 124 (d) 133
  36. 36.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) 22 (d) 66
  37. 37.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 324 (c) 294 (d) 334
  38. 38.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) 39 (b) 36 (c) 12 (d) 108
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 18 (b) 19 (c) 20 (d) 9
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 6 (b) 7 (c) 5 (d) 4

Answer key

  1. 24
  2. 57
  3. 2
  4. 21
  5. 6
  6. 48
  7. 8
  8. 339
  9. 175
  10. 115
  11. 45
  12. 6
  13. 27
  14. 18
  15. 9
  16. 627
  17. 73
  18. 60
  19. 4
  20. 17
  21. 8
  22. 567
  23. 3
  24. 4
  25. 408
  26. 354
  27. 18
  28. 4
  29. 3
  30. 15
  31. 582
  32. 42
  33. 5
  34. 15
  35. 133
  36. 66
  37. 333
  38. 36
  39. 19
  40. 6

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