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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 199 · 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.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
  2. 2.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) 69 (b) 66 (c) 22 (d) 198
  3. 3.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 404 (b) 489 (c) 498 (d) 499
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 19 (b) 20 (c) 9 (d) 21
  5. 5.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) 33 (c) 99 (d) 36
  6. 6.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  7. 7.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) 57 (d) 18
  8. 8.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 261 (c) 246 (d) 252
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 19 (b) 20 (c) 21 (d) 9
  10. 10.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
  11. 11.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 120 (c) 111 (d) 102
  12. 12.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) 30 (c) 10 (d) 33
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 63? (a) 6 (b) 5 (c) 4 (d) 7
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 63? (a) 4 (b) 7 (c) 5 (d) 6
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 17 (b) 18 (c) 19 (d) 7
  16. 16.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) 9 (c) 27 (d) 30
  17. 17.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 306 (c) 307 (d) 297
  18. 18.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 70 (c) 78 (d) 69
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 8 (b) 17 (c) 19 (d) 18
  20. 20.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
  21. 21.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 6 (d) 15
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  23. 23.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) 232 (d) 240
  24. 24.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) 48 (b) 45 (c) 15 (d) 135
  25. 25.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 288 (c) 325 (d) 324
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 14 (b) 16 (c) 15 (d) 5
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 96? (a) 20 (b) 21 (c) 9 (d) 19
  28. 28.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 16 (b) 7 (c) 18 (d) 17
  30. 30.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 68 (c) 78 (d) 77
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 2 (b) 3 (c) 4 (d) 5
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 21 (b) 20 (c) 19 (d) 9
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 89? (a) 20 (b) 18 (c) 8 (d) 19
  34. 34.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) 16 (b) 48 (c) 51 (d) 144
  35. 35.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 446 (b) 562 (c) 552 (d) 561
  36. 36.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
  37. 37.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  38. 38.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  39. 39.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) 24 (b) 216 (c) 72 (d) 75
  40. 40.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 382 (c) 456 (d) 465

Answer key

  1. 18
  2. 66
  3. 498
  4. 20
  5. 33
  6. 4
  7. 54
  8. 261
  9. 20
  10. 51
  11. 111
  12. 30
  13. 6
  14. 6
  15. 18
  16. 27
  17. 306
  18. 69
  19. 18
  20. 9
  21. 5
  22. 2
  23. 240
  24. 45
  25. 324
  26. 15
  27. 20
  28. 8
  29. 17
  30. 77
  31. 4
  32. 20
  33. 19
  34. 48
  35. 561
  36. 8
  37. 2
  38. 7
  39. 72
  40. 465

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