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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 792 · 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 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) 30 (c) 27 (d) 9
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 17 (b) 16 (c) 7 (d) 18
  3. 3.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) 12 (b) 39 (c) 36 (d) 108
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 14 (b) 4 (c) 15 (d) 16
  5. 5.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 412 (c) 501 (d) 511
  6. 6.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 58? (a) 17 (b) 5 (c) 15 (d) 16
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 18 (b) 19 (c) 17 (d) 7
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 20 (b) 8 (c) 19 (d) 18
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 4 (b) 2 (c) 1 (d) 3
  11. 11.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 2 (d) 3
  12. 12.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  13. 13.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) 22 (c) 69 (d) 66
  14. 14.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 8 (d) 6
  15. 15.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
  16. 16.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 609 (c) 600 (d) 478
  17. 17.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 232 (c) 240 (d) 241
  18. 18.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 337 (b) 296 (c) 327 (d) 336
  19. 19.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 155 (c) 146 (d) 164
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 13 (b) 14 (c) 15 (d) 3
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 16 (b) 6 (c) 17 (d) 18
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 6 (b) 16 (c) 17 (d) 18
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 14 (b) 16 (c) 4 (d) 15
  24. 24.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) 33 (c) 90 (d) 30
  25. 25.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 453 (c) 374 (d) 444
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 99? (a) 21 (b) 9 (c) 20 (d) 19
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 13 (b) 4 (c) 15 (d) 14
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 21 (b) 20 (c) 9 (d) 19
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 20 (b) 8 (c) 18 (d) 19
  30. 30.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) 21 (b) 7 (c) 24 (d) 63
  31. 31.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  32. 32.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 226 (c) 232 (d) 231
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 21 (b) 20 (c) 19 (d) 9
  34. 34.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 69 (c) 72 (d) 23
  35. 35.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 182 (c) 181 (d) 190
  36. 36.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
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 1 (d) 3
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 70? (a) 16 (b) 7 (c) 17 (d) 18
  39. 39.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 2 (b) 5 (c) 4 (d) 3

Answer key

  1. 27
  2. 17
  3. 36
  4. 15
  5. 510
  6. 4
  7. 16
  8. 18
  9. 19
  10. 3
  11. 2
  12. 6
  13. 66
  14. 7
  15. 5
  16. 609
  17. 240
  18. 336
  19. 155
  20. 14
  21. 17
  22. 17
  23. 15
  24. 30
  25. 453
  26. 20
  27. 14
  28. 20
  29. 19
  30. 21
  31. 5
  32. 231
  33. 20
  34. 69
  35. 181
  36. 60
  37. 3
  38. 17
  39. 7
  40. 4

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