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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 974 · 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 times is the digit 7 written when you write all the numbers from 1 to 40? (a) 5 (b) 3 (c) 2 (d) 4
  2. 2.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) 60 (b) 57 (c) 171 (d) 19
  3. 3.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  4. 4.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) 10 (b) 33 (c) 30 (d) 90
  5. 5.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  6. 6.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 14 (d) 7
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 2 (d) 1
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 9 (b) 4 (c) 8 (d) 6
  9. 9.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  10. 10.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  11. 11.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) 81 (b) 27 (c) 9 (d) 30
  12. 12.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) 162 (b) 18 (c) 54 (d) 57
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 18 (b) 16 (c) 17 (d) 6
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 6 (b) 3 (c) 4 (d) 5
  15. 15.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  16. 16.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  17. 17.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 46? (a) 4 (b) 5 (c) 3 (d) 2
  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) 45 (b) 5 (c) 15 (d) 18
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 18 (b) 17 (c) 19 (d) 7
  21. 21.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
  22. 22.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 248 (c) 265 (d) 264
  23. 23.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) 99 (d) 33
  24. 24.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 528 (b) 430 (c) 538 (d) 537
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 71? (a) 16 (b) 18 (c) 7 (d) 17
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 11 (b) 9 (c) 4 (d) 10
  27. 27.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) 39 (c) 13 (d) 42
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 7 (b) 18 (c) 19 (d) 17
  29. 29.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 279 (c) 289 (d) 264
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 74? (a) 19 (b) 7 (c) 17 (d) 18
  31. 31.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) 190 (c) 189 (d) 180
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 6 (b) 4 (c) 5 (d) 7
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 8 (b) 20 (c) 19 (d) 18
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 5 (b) 2 (c) 3 (d) 4
  35. 35.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
  36. 36.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) 24 (b) 72 (c) 27 (d) 8
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 3 (b) 5 (c) 2 (d) 4
  38. 38.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) 17 (b) 54 (c) 153 (d) 51
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 4 (b) 3 (c) 1 (d) 2
  40. 40.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) 63 (b) 66 (c) 21 (d) 189

Answer key

  1. 4
  2. 57
  3. 7
  4. 30
  5. 4
  6. 6
  7. 2
  8. 8
  9. 4
  10. 8
  11. 27
  12. 54
  13. 17
  14. 5
  15. 5
  16. 7
  17. 9
  18. 4
  19. 15
  20. 18
  21. 8
  22. 264
  23. 33
  24. 537
  25. 17
  26. 10
  27. 39
  28. 18
  29. 288
  30. 18
  31. 189
  32. 6
  33. 19
  34. 4
  35. 606
  36. 24
  37. 4
  38. 51
  39. 3
  40. 63

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