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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 784 · 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.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 555 (b) 448 (c) 564 (d) 565
  2. 2.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) 45 (b) 48 (c) 15 (d) 135
  3. 3.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) 30 (c) 90 (d) 33
  4. 4.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 283 (c) 282 (d) 260
  5. 5.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 14 (d) 7
  6. 6.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) 63 (c) 180 (d) 20
  7. 7.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 15 (b) 6 (c) 17 (d) 16
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 5 (b) 17 (c) 15 (d) 16
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 3 (b) 1 (c) 4 (d) 2
  11. 11.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 32 (c) 50 (d) 41
  12. 12.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) 7 (b) 24 (c) 63 (d) 21
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 16 (b) 17 (c) 7 (d) 18
  14. 14.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) 27 (c) 8 (d) 72
  15. 15.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 136 (c) 127 (d) 118
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 20 (b) 18 (c) 19 (d) 9
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 13 (b) 4 (c) 14 (d) 15
  18. 18.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) 21 (c) 18 (d) 6
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 16 (b) 14 (c) 15 (d) 4
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 59? (a) 16 (b) 5 (c) 15 (d) 17
  21. 21.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) 69 (b) 66 (c) 198 (d) 22
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 8 (b) 13 (c) 10 (d) 12
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 62? (a) 5 (b) 6 (c) 4 (d) 7
  24. 24.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 134 (c) 143 (d) 144
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 10 (b) 11 (c) 5 (d) 8
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 3 (b) 14 (c) 15 (d) 13
  27. 27.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 327 (c) 318 (d) 290
  28. 28.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 540 (c) 541 (d) 531
  29. 29.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  30. 30.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 19 (b) 7 (c) 17 (d) 18
  32. 32.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 2 (b) 5 (c) 4 (d) 3
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 8 (b) 18 (c) 17 (d) 19
  35. 35.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
  36. 36.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) 9 (c) 27 (d) 30
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 68? (a) 16 (b) 17 (c) 6 (d) 15
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 4 (b) 5 (c) 3 (d) 6
  39. 39.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 361 (b) 351 (c) 312 (d) 360
  40. 40.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 5 (d) 3

Answer key

  1. 564
  2. 45
  3. 30
  4. 282
  5. 6
  6. 60
  7. 3
  8. 16
  9. 16
  10. 3
  11. 41
  12. 21
  13. 17
  14. 24
  15. 127
  16. 19
  17. 14
  18. 18
  19. 15
  20. 16
  21. 66
  22. 12
  23. 6
  24. 143
  25. 10
  26. 14
  27. 327
  28. 540
  29. 3
  30. 6
  31. 18
  32. 2
  33. 4
  34. 18
  35. 8
  36. 27
  37. 16
  38. 5
  39. 360
  40. 4

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