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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 134 · 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 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) 108 (b) 39 (c) 12 (d) 36
  2. 2.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) 90 (c) 33 (d) 30
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 16 (b) 18 (c) 6 (d) 17
  5. 5.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 19 (b) 17 (c) 7 (d) 18
  7. 7.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) 81 (b) 30 (c) 9 (d) 27
  8. 8.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  9. 9.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 469 (c) 468 (d) 459
  10. 10.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 10 (d) 7
  11. 11.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 7 (b) 5 (c) 6 (d) 4
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 70? (a) 16 (b) 18 (c) 17 (d) 7
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 71? (a) 18 (b) 7 (c) 16 (d) 17
  16. 16.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  17. 17.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 478 (b) 610 (c) 600 (d) 609
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 2 (b) 5 (c) 4 (d) 3
  19. 19.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 132 (c) 150 (d) 141
  20. 20.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 2 (d) 1
  21. 21.The numbers 17 to 25 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) 189 (c) 63 (d) 66
  22. 22.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 570 (c) 580 (d) 458
  23. 23.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) 72 (d) 216
  24. 24.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) 7 (d) 63
  25. 25.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) 60 (c) 180 (d) 20
  26. 26.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) 621 (d) 612
  27. 27.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 58 (c) 66 (d) 57
  28. 28.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
  29. 29.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) 360 (c) 351 (d) 361
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 2 (b) 5 (c) 4 (d) 3
  31. 31.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 411 (c) 420 (d) 421
  32. 32.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 19 (b) 8 (c) 20 (d) 18
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 19 (d) 8
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 76? (a) 19 (b) 17 (c) 7 (d) 18
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 66? (a) 6 (b) 13 (c) 15 (d) 14
  37. 37.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) 11 (b) 99 (c) 33 (d) 36
  38. 38.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 483 (c) 484 (d) 394
  39. 39.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
  40. 40.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 589 (b) 579 (c) 464 (d) 588

Answer key

  1. 36
  2. 30
  3. 5
  4. 17
  5. 3
  6. 18
  7. 27
  8. 9
  9. 468
  10. 6
  11. 7
  12. 6
  13. 8
  14. 17
  15. 17
  16. 4
  17. 609
  18. 4
  19. 141
  20. 2
  21. 63
  22. 579
  23. 72
  24. 21
  25. 60
  26. 621
  27. 57
  28. 57
  29. 360
  30. 4
  31. 420
  32. 5
  33. 19
  34. 19
  35. 18
  36. 14
  37. 33
  38. 483
  39. 3
  40. 588

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