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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 497 · 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 9? (a) 8 (b) 9 (c) 10 (d) 11
  2. 2.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 427 (b) 356 (c) 417 (d) 426
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 88? (a) 8 (b) 18 (c) 19 (d) 20
  4. 4.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) 180 (b) 20 (c) 63 (d) 60
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 8 (b) 7 (c) 9 (d) 6
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 16 (b) 18 (c) 7 (d) 17
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 13 (b) 16 (c) 8 (d) 15
  8. 8.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 7 (d) 8
  9. 9.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 504 (b) 495 (c) 408 (d) 505
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 8 (b) 17 (c) 18 (d) 19
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 54? (a) 15 (b) 16 (c) 5 (d) 17
  12. 12.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) 66 (b) 22 (c) 198 (d) 69
  13. 13.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) 19 (b) 171 (c) 57 (d) 60
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 16 (b) 6 (c) 18 (d) 17
  15. 15.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 591 (c) 592 (d) 582
  16. 16.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 162 (c) 18 (d) 54
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 13 (b) 12 (c) 10 (d) 9
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 16 (b) 14 (c) 4 (d) 15
  19. 19.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 6 (d) 15
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 6 (b) 5 (c) 3 (d) 4
  21. 21.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) 24 (c) 21 (d) 7
  22. 22.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 267 (b) 276 (c) 277 (d) 256
  23. 23.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) 108 (c) 36 (d) 12
  24. 24.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
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 98? (a) 20 (b) 9 (c) 21 (d) 19
  26. 26.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) 14 (b) 45 (c) 42 (d) 126
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 15 (b) 4 (c) 16 (d) 14
  28. 28.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) 66 (b) 189 (c) 21 (d) 63
  29. 29.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 120 (c) 119 (d) 128
  30. 30.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) 342 (c) 343 (d) 333
  31. 31.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
  32. 32.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) 9 (b) 81 (c) 30 (d) 27
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 90? (a) 19 (b) 20 (c) 18 (d) 9
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 19 (b) 18 (c) 7 (d) 17
  35. 35.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) 15 (c) 48 (d) 135
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 18 (b) 17 (c) 8 (d) 19
  37. 37.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) 17 (b) 153 (c) 54 (d) 51
  38. 38.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) 90 (b) 10 (c) 30 (d) 33
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 6 (b) 4 (c) 7 (d) 5
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 6 (b) 18 (c) 17 (d) 16

Answer key

  1. 9
  2. 426
  3. 19
  4. 60
  5. 8
  6. 17
  7. 15
  8. 8
  9. 504
  10. 18
  11. 16
  12. 66
  13. 57
  14. 17
  15. 591
  16. 54
  17. 12
  18. 15
  19. 5
  20. 5
  21. 21
  22. 276
  23. 36
  24. 16
  25. 20
  26. 42
  27. 15
  28. 63
  29. 119
  30. 342
  31. 24
  32. 27
  33. 19
  34. 18
  35. 45
  36. 18
  37. 51
  38. 30
  39. 6
  40. 17

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