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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 886 · 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 3 written when you write all the numbers from 1 to 78? (a) 19 (b) 17 (c) 7 (d) 18
  2. 2.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
  3. 3.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 12 (b) 3 (c) 13 (d) 14
  5. 5.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) 19 (b) 60 (c) 57 (d) 171
  6. 6.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) 27 (b) 24 (c) 8 (d) 72
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  9. 9.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
  10. 10.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 198 (c) 189 (d) 180
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 2 (b) 5 (c) 3 (d) 4
  12. 12.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) 414 (c) 354 (d) 424
  13. 13.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
  14. 14.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) 15 (c) 5 (d) 18
  15. 15.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) 90 (c) 30 (d) 33
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 16 (b) 18 (c) 17 (d) 6
  17. 17.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 17 (d) 4
  18. 18.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) 7 (d) 24
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 7 (b) 18 (c) 19 (d) 17
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 96? (a) 19 (b) 9 (c) 21 (d) 20
  21. 21.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) 24 (c) 75 (d) 72
  22. 22.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 64 (c) 54 (d) 63
  23. 23.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
  24. 24.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 207 (c) 23 (d) 72
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 58? (a) 5 (b) 17 (c) 16 (d) 15
  26. 26.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) 54 (b) 17 (c) 153 (d) 51
  27. 27.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  28. 28.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 382 (c) 326 (d) 381
  29. 29.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 241 (c) 240 (d) 232
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 8 (b) 9 (c) 6 (d) 4
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 71? (a) 18 (b) 16 (c) 17 (d) 7
  32. 32.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) 16 (c) 51 (d) 144
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 54? (a) 5 (b) 16 (c) 17 (d) 15
  34. 34.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 33 (b) 24 (c) 42 (d) 34
  35. 35.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  36. 36.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 139 (b) 130 (c) 148 (d) 140
  37. 37.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 50 (c) 59 (d) 60
  38. 38.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 270 (c) 279 (d) 280
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 7 (b) 6 (c) 9 (d) 10
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 53? (a) 16 (b) 5 (c) 15 (d) 14

Answer key

  1. 18
  2. 7
  3. 2
  4. 13
  5. 57
  6. 24
  7. 4
  8. 5
  9. 2
  10. 189
  11. 4
  12. 423
  13. 9
  14. 15
  15. 30
  16. 17
  17. 3
  18. 21
  19. 18
  20. 20
  21. 72
  22. 63
  23. 63
  24. 69
  25. 16
  26. 51
  27. 4
  28. 381
  29. 240
  30. 8
  31. 17
  32. 48
  33. 16
  34. 33
  35. 8
  36. 139
  37. 59
  38. 279
  39. 9
  40. 15

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