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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 344 · 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 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 180 (c) 190 (d) 189
  2. 2.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 555 (b) 556 (c) 442 (d) 546
  3. 3.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) 23 (b) 72 (c) 69 (d) 207
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 18 (b) 17 (c) 19 (d) 8
  5. 5.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 56 (c) 47 (d) 38
  6. 6.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 266 (c) 291 (d) 282
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 50? (a) 5 (b) 4 (c) 6 (d) 3
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 19 (b) 20 (c) 18 (d) 9
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 7 (b) 17 (c) 19 (d) 18
  10. 10.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 296 (b) 327 (c) 337 (d) 336
  11. 11.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  12. 12.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 13 (d) 6
  13. 13.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) 135 (b) 15 (c) 48 (d) 45
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 79? (a) 7 (b) 19 (c) 17 (d) 18
  15. 15.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) 19 (d) 57
  16. 16.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  17. 17.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) 30 (b) 9 (c) 27 (d) 81
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 8 (b) 6 (c) 7 (d) 9
  19. 19.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) 18 (b) 15 (c) 5 (d) 45
  20. 20.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 502 (b) 492 (c) 406 (d) 501
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 8 (b) 18 (c) 17 (d) 19
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 2 (b) 5 (c) 3 (d) 4
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 9 (d) 20
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 21 (b) 9 (c) 19 (d) 20
  25. 25.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) 7 (c) 21 (d) 24
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 96? (a) 20 (b) 21 (c) 9 (d) 19
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 4 (b) 1 (c) 3 (d) 2
  28. 28.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) 6 (b) 54 (c) 18 (d) 21
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 75? (a) 6 (b) 5 (c) 7 (d) 8
  30. 30.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 2 (d) 4
  31. 31.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 102 (c) 120 (d) 111
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 6 (b) 12 (c) 11 (d) 9
  33. 33.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 162 (c) 171 (d) 172
  34. 34.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 3 (d) 17
  35. 35.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  36. 36.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 57 (c) 66 (d) 48
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 63? (a) 7 (b) 4 (c) 5 (d) 6
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 9 (d) 20
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 17 (b) 18 (c) 6 (d) 16
  40. 40.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) 54 (d) 18

Answer key

  1. 189
  2. 555
  3. 69
  4. 18
  5. 47
  6. 291
  7. 5
  8. 19
  9. 18
  10. 336
  11. 5
  12. 7
  13. 45
  14. 18
  15. 57
  16. 6
  17. 27
  18. 8
  19. 15
  20. 501
  21. 18
  22. 4
  23. 20
  24. 20
  25. 21
  26. 20
  27. 3
  28. 18
  29. 7
  30. 3
  31. 111
  32. 11
  33. 171
  34. 3
  35. 4
  36. 57
  37. 6
  38. 20
  39. 17
  40. 54

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