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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 979 · 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 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) 171 (b) 60 (c) 57 (d) 19
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 20 (b) 18 (c) 19 (d) 8
  3. 3.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) 63 (b) 21 (c) 66 (d) 189
  4. 4.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  5. 5.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 63 (c) 64 (d) 54
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 14 (b) 15 (c) 16 (d) 5
  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) 27 (c) 9 (d) 30
  8. 8.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) 126 (c) 45 (d) 14
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 15 (b) 14 (c) 4 (d) 16
  10. 10.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 32 (c) 41 (d) 42
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 51? (a) 5 (b) 14 (c) 15 (d) 16
  12. 12.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 34 (c) 43 (d) 52
  13. 13.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) 27 (b) 24 (c) 72 (d) 8
  14. 14.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
  15. 15.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) 33 (b) 11 (c) 99 (d) 36
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 18 (b) 19 (c) 9 (d) 20
  17. 17.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 297 (c) 298 (d) 270
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 4 (b) 14 (c) 13 (d) 12
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 4 (b) 5 (c) 6 (d) 3
  20. 20.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 57 (b) 48 (c) 66 (d) 58
  21. 21.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  22. 22.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 529 (b) 528 (c) 519 (d) 424
  23. 23.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) 6 (c) 54 (d) 18
  24. 24.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 111 (b) 102 (c) 112 (d) 120
  25. 25.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 360 (c) 370 (d) 369
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 87? (a) 20 (b) 8 (c) 19 (d) 18
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 14 (b) 4 (c) 16 (d) 15
  28. 28.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 15 (b) 14 (c) 4 (d) 13
  30. 30.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) 153 (c) 51 (d) 17
  31. 31.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) 45 (c) 18 (d) 15
  32. 32.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
  33. 33.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 343 (c) 342 (d) 333
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 17 (b) 18 (c) 19 (d) 7
  35. 35.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 5 (d) 3
  36. 36.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
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 50? (a) 6 (b) 3 (c) 4 (d) 5
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 19 (d) 8
  39. 39.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 5 (d) 15
  40. 40.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 155 (b) 146 (c) 164 (d) 156

Answer key

  1. 57
  2. 19
  3. 63
  4. 6
  5. 63
  6. 15
  7. 27
  8. 42
  9. 15
  10. 41
  11. 15
  12. 43
  13. 24
  14. 5
  15. 33
  16. 19
  17. 297
  18. 13
  19. 5
  20. 57
  21. 3
  22. 528
  23. 18
  24. 111
  25. 369
  26. 19
  27. 15
  28. 9
  29. 14
  30. 51
  31. 15
  32. 8
  33. 342
  34. 18
  35. 4
  36. 495
  37. 5
  38. 19
  39. 5
  40. 155

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