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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 304 · 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 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) 57 (c) 19 (d) 60
  2. 2.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) 108 (d) 36
  3. 3.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) 48 (b) 144 (c) 16 (d) 51
  4. 4.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 476 (b) 597 (c) 606 (d) 607
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 77? (a) 8 (b) 7 (c) 5 (d) 6
  6. 6.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
  7. 7.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) 39 (b) 42 (c) 117 (d) 13
  8. 8.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 315 (c) 325 (d) 288
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 54? (a) 5 (b) 3 (c) 4 (d) 6
  10. 10.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  11. 11.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  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) 198 (c) 22 (d) 69
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 73? (a) 9 (b) 12 (c) 11 (d) 7
  14. 14.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) 42 (b) 126 (c) 45 (d) 14
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 18 (b) 7 (c) 17 (d) 19
  16. 16.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 6 (d) 13
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 97? (a) 21 (b) 9 (c) 19 (d) 20
  18. 18.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 4 (b) 6 (c) 5 (d) 7
  20. 20.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 42? (a) 2 (b) 4 (c) 3 (d) 5
  22. 22.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) 21 (c) 63 (d) 189
  23. 23.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) 15 (b) 5 (c) 45 (d) 18
  24. 24.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  25. 25.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 4 (b) 3 (c) 6 (d) 5
  27. 27.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) 90 (d) 10
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 76? (a) 5 (b) 7 (c) 8 (d) 6
  29. 29.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) 60 (b) 180 (c) 20 (d) 63
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 94? (a) 21 (b) 20 (c) 19 (d) 9
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 15 (b) 17 (c) 9 (d) 18
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 16 (b) 6 (c) 18 (d) 17
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 6 (b) 16 (c) 17 (d) 15
  34. 34.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  35. 35.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
  36. 36.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 405 (c) 414 (d) 415
  37. 37.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 494 (c) 634 (d) 624
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 16 (b) 15 (c) 5 (d) 17
  39. 39.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 147 (c) 156 (d) 138
  40. 40.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 198 (c) 189 (d) 180

Answer key

  1. 57
  2. 36
  3. 48
  4. 606
  5. 7
  6. 161
  7. 39
  8. 324
  9. 5
  10. 2
  11. 3
  12. 66
  13. 11
  14. 42
  15. 18
  16. 7
  17. 20
  18. 9
  19. 6
  20. 6
  21. 4
  22. 63
  23. 15
  24. 2
  25. 7
  26. 5
  27. 30
  28. 7
  29. 60
  30. 20
  31. 17
  32. 17
  33. 16
  34. 5
  35. 3
  36. 414
  37. 633
  38. 16
  39. 147
  40. 189

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