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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 9 · 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 3? (a) 2 (b) 10 (c) 4 (d) 3
  2. 2.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) 81 (d) 27
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 4 (b) 15 (c) 14 (d) 13
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 15 (b) 17 (c) 5 (d) 16
  5. 5.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 152 (c) 161 (d) 162
  6. 6.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  7. 7.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  8. 8.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 10 (d) 6
  9. 9.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  10. 10.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 376 (c) 375 (d) 366
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 2 (b) 4 (c) 3 (d) 5
  12. 12.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 616 (c) 606 (d) 482
  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) 22 (b) 66 (c) 198 (d) 69
  14. 14.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) 48 (b) 15 (c) 45 (d) 135
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 4 (b) 14 (c) 15 (d) 16
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 16 (b) 4 (c) 14 (d) 15
  17. 17.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) 51 (b) 17 (c) 54 (d) 153
  18. 18.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) 63 (d) 21
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 15 (b) 4 (c) 14 (d) 16
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  21. 21.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) 36 (c) 33 (d) 11
  22. 22.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
  23. 23.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 86 (c) 96 (d) 95
  24. 24.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 7 (d) 5
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 8 (b) 19 (c) 20 (d) 18
  26. 26.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 1 (d) 18
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 17 (b) 18 (c) 16 (d) 6
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 16 (b) 15 (c) 4 (d) 14
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 63? (a) 5 (b) 4 (c) 7 (d) 6
  30. 30.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 445 (c) 444 (d) 368
  31. 31.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 110 (c) 102 (d) 101
  32. 32.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  33. 33.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
  34. 34.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 376 (c) 456 (d) 457
  35. 35.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 106 (c) 88 (d) 97
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 14 (b) 15 (c) 16 (d) 5
  37. 37.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) 30 (b) 33 (c) 10 (d) 90
  38. 38.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) 21 (c) 24 (d) 63
  39. 39.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) 20 (b) 63 (c) 60 (d) 180
  40. 40.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 244 (c) 259 (d) 258

Answer key

  1. 3
  2. 27
  3. 14
  4. 16
  5. 161
  6. 5
  7. 4
  8. 7
  9. 8
  10. 375
  11. 4
  12. 615
  13. 66
  14. 45
  15. 15
  16. 15
  17. 51
  18. 63
  19. 15
  20. 4
  21. 33
  22. 36
  23. 95
  24. 6
  25. 19
  26. 2
  27. 17
  28. 15
  29. 6
  30. 444
  31. 101
  32. 2
  33. 42
  34. 456
  35. 97
  36. 15
  37. 30
  38. 21
  39. 60
  40. 258

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