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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 602 · 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 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
  2. 2.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
  3. 3.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) 36 (b) 11 (c) 33 (d) 99
  4. 4.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 152 (c) 142 (d) 151
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 7 (b) 18 (c) 19 (d) 17
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 17 (b) 15 (c) 16 (d) 5
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 78? (a) 18 (b) 7 (c) 19 (d) 17
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 4 (b) 5 (c) 3 (d) 6
  9. 9.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) 51 (b) 16 (c) 144 (d) 48
  10. 10.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 62 (c) 61 (d) 70
  11. 11.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 15 (b) 14 (c) 13 (d) 3
  13. 13.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 424 (c) 354 (d) 414
  14. 14.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) 21 (b) 18 (c) 6 (d) 54
  15. 15.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 18 (b) 6 (c) 16 (d) 17
  17. 17.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 8 (d) 13
  18. 18.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) 72 (b) 24 (c) 8 (d) 27
  19. 19.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 415 (b) 348 (c) 405 (d) 414
  20. 20.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 93 (b) 84 (c) 94 (d) 102
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 5 (b) 7 (c) 6 (d) 8
  22. 22.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 10 (d) 9
  23. 23.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
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 13 (b) 3 (c) 15 (d) 14
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 5 (b) 2 (c) 3 (d) 4
  26. 26.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
  27. 27.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
  28. 28.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 99? (a) 9 (b) 21 (c) 19 (d) 20
  30. 30.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) 117 (c) 39 (d) 13
  31. 31.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) 90 (c) 33 (d) 10
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 9 (b) 21 (c) 20 (d) 19
  33. 33.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 259 (b) 258 (c) 249 (d) 244
  34. 34.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 132 (c) 131 (d) 140
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 66? (a) 7 (b) 5 (c) 6 (d) 4
  36. 36.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) 81 (c) 30 (d) 27
  37. 37.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  38. 38.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  39. 39.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  40. 40.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) 69 (d) 198

Answer key

  1. 72
  2. 6
  3. 33
  4. 151
  5. 18
  6. 16
  7. 18
  8. 5
  9. 48
  10. 61
  11. 3
  12. 14
  13. 423
  14. 18
  15. 5
  16. 17
  17. 7
  18. 24
  19. 414
  20. 93
  21. 7
  22. 8
  23. 42
  24. 14
  25. 4
  26. 7
  27. 21
  28. 4
  29. 20
  30. 39
  31. 30
  32. 20
  33. 258
  34. 131
  35. 6
  36. 27
  37. 4
  38. 9
  39. 2
  40. 66

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