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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 818 · 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 2 written when you write all the numbers from 1 to 69? (a) 6 (b) 16 (c) 18 (d) 17
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 11 (b) 12 (c) 5 (d) 13
  3. 3.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) 15 (b) 135 (c) 48 (d) 45
  4. 4.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) 27 (c) 8 (d) 24
  5. 5.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) 63 (b) 21 (c) 7 (d) 24
  6. 6.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  7. 7.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
  8. 8.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
  9. 9.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 18 (b) 17 (c) 7 (d) 19
  11. 11.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
  12. 12.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 502 (b) 501 (c) 406 (d) 492
  13. 13.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
  14. 14.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  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) 90 (b) 33 (c) 10 (d) 30
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 91? (a) 9 (b) 18 (c) 19 (d) 20
  17. 17.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 160 (c) 169 (d) 170
  18. 18.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 198 (c) 189 (d) 199
  19. 19.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 81 (c) 90 (d) 72
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 1 (b) 2 (c) 4 (d) 3
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 2 (b) 5 (c) 4 (d) 3
  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) 18 (b) 54 (c) 6 (d) 21
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 4 (b) 1 (c) 2 (d) 3
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 19 (b) 18 (c) 8 (d) 20
  25. 25.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) 22 (c) 69 (d) 66
  26. 26.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 246 (c) 261 (d) 262
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  28. 28.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) 66 (b) 189 (c) 63 (d) 21
  29. 29.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) 5 (b) 18 (c) 15 (d) 45
  30. 30.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  31. 31.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6
  32. 32.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 122 (c) 131 (d) 132
  33. 33.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 366 (c) 442 (d) 441
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 92? (a) 18 (b) 9 (c) 19 (d) 20
  35. 35.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 91 (c) 92 (d) 100
  36. 36.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 7 (d) 9
  37. 37.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  38. 38.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 303 (c) 274 (d) 304
  39. 39.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) 144 (b) 48 (c) 51 (d) 16
  40. 40.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 39 (b) 48 (c) 30 (d) 40

Answer key

  1. 17
  2. 12
  3. 45
  4. 24
  5. 21
  6. 5
  7. 5
  8. 3
  9. 4
  10. 18
  11. 8
  12. 501
  13. 9
  14. 6
  15. 30
  16. 19
  17. 169
  18. 198
  19. 81
  20. 3
  21. 4
  22. 18
  23. 3
  24. 19
  25. 66
  26. 261
  27. 2
  28. 63
  29. 15
  30. 9
  31. 6
  32. 131
  33. 441
  34. 19
  35. 91
  36. 8
  37. 4
  38. 303
  39. 48
  40. 39

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