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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 490 · 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 15? (a) 16 (b) 5 (c) 3 (d) 4
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 20 (b) 19 (c) 9 (d) 18
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 16 (b) 4 (c) 15 (d) 14
  4. 4.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) 54 (b) 6 (c) 18 (d) 21
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 4 (b) 3 (c) 5 (d) 2
  6. 6.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) 33 (b) 30 (c) 10 (d) 90
  7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 65? (a) 18 (b) 6 (c) 17 (d) 16
  8. 8.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 9 (d) 8
  9. 9.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 342 (c) 343 (d) 300
  10. 10.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 188 (c) 170 (d) 179
  11. 11.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) 11 (c) 33 (d) 36
  12. 12.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 58 (c) 40 (d) 49
  13. 13.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) 101 (d) 102
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 14 (b) 15 (c) 4 (d) 16
  15. 15.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 350 (b) 418 (c) 417 (d) 408
  16. 16.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) 18 (c) 5 (d) 45
  17. 17.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) 189 (b) 66 (c) 21 (d) 63
  18. 18.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) 54 (b) 18 (c) 162 (d) 57
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 20 (b) 18 (c) 19 (d) 9
  20. 20.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 38? (a) 3 (b) 2 (c) 4 (d) 5
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 85? (a) 18 (b) 20 (c) 8 (d) 19
  23. 23.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) 19 (c) 171 (d) 57
  24. 24.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) 8 (b) 27 (c) 24 (d) 72
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 16 (b) 17 (c) 18 (d) 6
  26. 26.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 630 (b) 498 (c) 639 (d) 640
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 18 (b) 17 (c) 8 (d) 19
  29. 29.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) 27 (b) 30 (c) 81 (d) 9
  30. 30.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  31. 31.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
  32. 32.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 198 (c) 210 (d) 207
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 6 (b) 18 (c) 16 (d) 17
  34. 34.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
  35. 35.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
  36. 36.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) 51 (c) 144 (d) 16
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 2 (b) 4 (c) 1 (d) 3
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 4 (b) 2 (c) 3 (d) 5
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 4 (b) 5 (c) 6 (d) 3
  40. 40.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5

Answer key

  1. 4
  2. 19
  3. 15
  4. 18
  5. 4
  6. 30
  7. 17
  8. 8
  9. 342
  10. 179
  11. 33
  12. 49
  13. 101
  14. 15
  15. 417
  16. 15
  17. 63
  18. 54
  19. 19
  20. 7
  21. 4
  22. 19
  23. 57
  24. 24
  25. 17
  26. 639
  27. 2
  28. 18
  29. 27
  30. 3
  31. 8
  32. 207
  33. 17
  34. 5
  35. 9
  36. 48
  37. 3
  38. 4
  39. 5
  40. 4

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