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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 24 · 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.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 13 (d) 6
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 17 (b) 15 (c) 5 (d) 16
  3. 3.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) 45 (b) 14 (c) 42 (d) 126
  4. 4.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 70 (c) 88 (d) 79
  5. 5.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 8 (d) 10
  6. 6.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) 153 (b) 17 (c) 54 (d) 51
  7. 7.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) 12 (c) 39 (d) 108
  8. 8.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  9. 9.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) 334 (c) 324 (d) 294
  10. 10.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) 18 (b) 15 (c) 5 (d) 45
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 60? (a) 15 (b) 17 (c) 16 (d) 6
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 84? (a) 8 (b) 20 (c) 19 (d) 18
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 6 (b) 17 (c) 16 (d) 18
  15. 15.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) 33 (b) 30 (c) 10 (d) 90
  16. 16.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) 480 (c) 603 (d) 613
  17. 17.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 496 (b) 486 (c) 495 (d) 402
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 18 (b) 19 (c) 7 (d) 17
  19. 19.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 7 (d) 9
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 9 (b) 20 (c) 18 (d) 19
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 4 (b) 14 (c) 15 (d) 13
  22. 22.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 68 (c) 60 (d) 59
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 9 (b) 6 (c) 5 (d) 8
  24. 24.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 298 (c) 330 (d) 340
  25. 25.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 6 (b) 4 (c) 3 (d) 5
  27. 27.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) 72 (b) 8 (c) 24 (d) 27
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 19 (b) 7 (c) 17 (d) 18
  29. 29.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 112 (c) 120 (d) 111
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 4 (b) 3 (c) 6 (d) 5
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 9 (d) 20
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 7 (b) 9 (c) 10 (d) 5
  33. 33.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) 48 (c) 16 (d) 51
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 3 (b) 4 (c) 5 (d) 6
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 8 (b) 18 (c) 19 (d) 17
  36. 36.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 74 (c) 82 (d) 73
  37. 37.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 3 (d) 1
  38. 38.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) 588 (c) 464 (d) 579
  39. 39.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 516 (c) 517 (d) 416
  40. 40.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11

Answer key

  1. 7
  2. 16
  3. 42
  4. 79
  5. 7
  6. 51
  7. 36
  8. 9
  9. 333
  10. 15
  11. 16
  12. 5
  13. 19
  14. 17
  15. 30
  16. 612
  17. 495
  18. 18
  19. 8
  20. 19
  21. 14
  22. 59
  23. 8
  24. 339
  25. 2
  26. 5
  27. 24
  28. 18
  29. 111
  30. 5
  31. 20
  32. 9
  33. 48
  34. 5
  35. 18
  36. 73
  37. 2
  38. 588
  39. 516
  40. 9

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