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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 213 · 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 10? (a) 8 (b) 10 (c) 9 (d) 11
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 4 (b) 2 (c) 5 (d) 3
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 2 (b) 5 (c) 4 (d) 3
  4. 4.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) 20 (c) 180 (d) 63
  5. 5.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 63? (a) 4 (b) 7 (c) 5 (d) 6
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 14 (b) 13 (c) 15 (d) 3
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 15 (b) 16 (c) 4 (d) 14
  9. 9.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) 54 (c) 153 (d) 17
  10. 10.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) 216 (b) 72 (c) 24 (d) 75
  11. 11.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 309 (c) 319 (d) 284
  12. 12.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 82 (c) 81 (d) 72
  13. 13.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  14. 14.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) 57 (b) 60 (c) 19 (d) 171
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 16 (b) 15 (c) 4 (d) 14
  16. 16.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) 21 (b) 189 (c) 63 (d) 66
  17. 17.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 156 (c) 155 (d) 146
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 20 (b) 21 (c) 9 (d) 19
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 14 (b) 13 (c) 15 (d) 3
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 56? (a) 5 (b) 4 (c) 7 (d) 6
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 3 (b) 2 (c) 4 (d) 5
  22. 22.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) 18 (c) 21 (d) 54
  23. 23.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) 117 (b) 42 (c) 39 (d) 13
  24. 24.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
  25. 25.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) 8 (c) 27 (d) 24
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 6 (b) 5 (c) 4 (d) 7
  27. 27.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 476 (c) 597 (d) 607
  28. 28.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 61 (c) 62 (d) 52
  29. 29.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 10 (d) 8
  30. 30.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 344 (b) 399 (c) 408 (d) 409
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 19 (b) 21 (c) 9 (d) 20
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 14 (b) 3 (c) 13 (d) 12
  33. 33.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 13 (d) 6
  34. 34.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) 54 (c) 162 (d) 18
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 21 (d) 19
  36. 36.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 6 (b) 3 (c) 4 (d) 5
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 18 (b) 19 (c) 17 (d) 7
  39. 39.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) 24 (c) 63 (d) 7
  40. 40.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 6 (d) 15

Answer key

  1. 9
  2. 4
  3. 4
  4. 60
  5. 4
  6. 6
  7. 14
  8. 15
  9. 51
  10. 72
  11. 318
  12. 81
  13. 9
  14. 57
  15. 15
  16. 63
  17. 155
  18. 20
  19. 14
  20. 6
  21. 4
  22. 18
  23. 39
  24. 6
  25. 24
  26. 6
  27. 606
  28. 61
  29. 7
  30. 408
  31. 20
  32. 13
  33. 7
  34. 54
  35. 20
  36. 6
  37. 5
  38. 18
  39. 21
  40. 5

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