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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 464 · 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 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) 54 (b) 162 (c) 18 (d) 57
  2. 2.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 41 (b) 32 (c) 42 (d) 50
  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) 90 (b) 10 (c) 33 (d) 30
  4. 4.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 3 (b) 5 (c) 4 (d) 6
  6. 6.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) 198 (b) 69 (c) 66 (d) 22
  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) 39 (c) 12 (d) 108
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 2 (b) 3 (c) 5 (d) 4
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 17 (b) 6 (c) 16 (d) 18
  10. 10.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) 30 (c) 81 (d) 27
  11. 11.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 154 (c) 153 (d) 144
  12. 12.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 349 (b) 348 (c) 339 (d) 304
  13. 13.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
  14. 14.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) 16 (b) 144 (c) 48 (d) 51
  15. 15.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 340 (b) 403 (c) 393 (d) 402
  16. 16.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 97 (b) 98 (c) 106 (d) 88
  17. 17.The numbers 9 to 17 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) 13 (c) 39 (d) 117
  18. 18.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) 75 (b) 72 (c) 216 (d) 24
  19. 19.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
  20. 20.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
  21. 21.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 252 (c) 261 (d) 262
  22. 22.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 15 (b) 6 (c) 17 (d) 16
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 3 (b) 15 (c) 13 (d) 14
  25. 25.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) 99 (b) 33 (c) 11 (d) 36
  26. 26.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) 8 (c) 72 (d) 24
  27. 27.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 68? (a) 8 (b) 6 (c) 5 (d) 7
  29. 29.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  30. 30.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  31. 31.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) 66 (c) 58 (d) 48
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 20 (d) 9
  33. 33.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 356 (c) 427 (d) 426
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 70? (a) 17 (b) 7 (c) 18 (d) 16
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 50? (a) 3 (b) 4 (c) 5 (d) 6
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 90? (a) 19 (b) 18 (c) 20 (d) 9
  37. 37.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) 180 (c) 60 (d) 20
  38. 38.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 88 (c) 80 (d) 79
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 6 (b) 3 (c) 5 (d) 4
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 20 (b) 9 (c) 18 (d) 19

Answer key

  1. 54
  2. 41
  3. 30
  4. 2
  5. 5
  6. 66
  7. 36
  8. 4
  9. 17
  10. 27
  11. 153
  12. 348
  13. 3
  14. 48
  15. 402
  16. 97
  17. 39
  18. 72
  19. 4
  20. 9
  21. 261
  22. 5
  23. 16
  24. 14
  25. 33
  26. 24
  27. 7
  28. 7
  29. 3
  30. 6
  31. 57
  32. 20
  33. 426
  34. 17
  35. 5
  36. 19
  37. 60
  38. 79
  39. 5
  40. 19

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