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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 727 · 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 11? (a) 12 (b) 8 (c) 7 (d) 9
  2. 2.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 123 (c) 124 (d) 132
  3. 3.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 16 (b) 15 (c) 4 (d) 14
  5. 5.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 15 (b) 17 (c) 16 (d) 5
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 17 (b) 18 (c) 6 (d) 16
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 54? (a) 5 (b) 16 (c) 17 (d) 15
  9. 9.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) 18 (b) 15 (c) 5 (d) 45
  10. 10.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 55 (c) 64 (d) 56
  11. 11.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 15 (c) 45 (d) 48
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 97? (a) 9 (b) 20 (c) 19 (d) 21
  13. 13.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 5 (d) 10
  14. 14.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) 30 (b) 27 (c) 81 (d) 9
  15. 15.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) 36 (b) 39 (c) 108 (d) 12
  16. 16.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) 54 (c) 18 (d) 57
  17. 17.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) 75 (c) 72 (d) 24
  18. 18.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) 45 (c) 126 (d) 14
  19. 19.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  20. 20.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 325 (b) 324 (c) 315 (d) 288
  21. 21.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 88 (c) 97 (d) 98
  22. 22.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) 11 (b) 36 (c) 99 (d) 33
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 10 (b) 11 (c) 5 (d) 8
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 9 (b) 19 (c) 18 (d) 20
  25. 25.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 504 (c) 414 (d) 514
  26. 26.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) 21 (c) 189 (d) 66
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 17 (b) 18 (c) 19 (d) 7
  28. 28.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 10 (d) 1
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 5 (b) 2 (c) 4 (d) 3
  30. 30.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 72 (c) 54 (d) 63
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 4 (b) 5 (c) 7 (d) 6
  32. 32.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
  33. 33.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) 63 (c) 24 (d) 7
  34. 34.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  35. 35.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  36. 36.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 51? (a) 16 (b) 15 (c) 5 (d) 14
  38. 38.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) 198 (b) 66 (c) 22 (d) 69
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 6 (b) 8 (c) 7 (d) 5
  40. 40.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 284 (b) 318 (c) 309 (d) 319

Answer key

  1. 8
  2. 123
  3. 6
  4. 15
  5. 3
  6. 16
  7. 17
  8. 16
  9. 15
  10. 55
  11. 45
  12. 20
  13. 4
  14. 27
  15. 36
  16. 54
  17. 72
  18. 42
  19. 4
  20. 324
  21. 97
  22. 33
  23. 10
  24. 19
  25. 513
  26. 63
  27. 18
  28. 2
  29. 4
  30. 63
  31. 6
  32. 9
  33. 21
  34. 5
  35. 9
  36. 6
  37. 15
  38. 66
  39. 7
  40. 318

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