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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 50 · 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 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) 171 (b) 57 (c) 60 (d) 19
  2. 2.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 472 (c) 601 (d) 600
  3. 3.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 252 (c) 262 (d) 261
  4. 4.The numbers 16 to 24 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) 63 (c) 180 (d) 20
  5. 5.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 6 (d) 7
  6. 6.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  7. 7.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 439 (c) 438 (d) 429
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 4 (d) 6
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 81? (a) 17 (b) 8 (c) 19 (d) 18
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 16 (b) 18 (c) 17 (d) 6
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 9 (b) 21 (c) 19 (d) 20
  12. 12.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 125 (b) 126 (c) 116 (d) 134
  13. 13.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) 24 (b) 72 (c) 8 (d) 27
  14. 14.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
  15. 15.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) 36 (b) 99 (c) 33 (d) 11
  16. 16.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 10 (d) 6
  17. 17.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
  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) 45 (b) 42 (c) 14 (d) 126
  19. 19.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) 5 (c) 15 (d) 18
  20. 20.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 118 (c) 136 (d) 127
  21. 21.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 525 (b) 516 (c) 526 (d) 422
  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) 64 (b) 63 (c) 54 (d) 72
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 17 (b) 6 (c) 15 (d) 16
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 4 (b) 3 (c) 5 (d) 6
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 15 (b) 17 (c) 16 (d) 5
  26. 26.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) 12 (c) 108 (d) 39
  27. 27.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) 23 (b) 69 (c) 207 (d) 72
  28. 28.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
  29. 29.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) 10 (c) 30 (d) 90
  30. 30.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) 66 (c) 21 (d) 189
  31. 31.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
  32. 32.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 5 (d) 7
  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) 63 (b) 7 (c) 24 (d) 21
  34. 34.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
  35. 35.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 101 (c) 92 (d) 110
  36. 36.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 230 (b) 228 (c) 238 (d) 237
  37. 37.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 270 (c) 279 (d) 258
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 7 (b) 5 (c) 4 (d) 6
  39. 39.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) 9 (c) 27 (d) 81
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 5 (b) 3 (c) 2 (d) 4

Answer key

  1. 57
  2. 600
  3. 261
  4. 60
  5. 7
  6. 9
  7. 438
  8. 5
  9. 18
  10. 17
  11. 20
  12. 125
  13. 24
  14. 8
  15. 33
  16. 7
  17. 4
  18. 42
  19. 15
  20. 127
  21. 525
  22. 63
  23. 16
  24. 5
  25. 16
  26. 36
  27. 69
  28. 45
  29. 30
  30. 63
  31. 66
  32. 6
  33. 21
  34. 3
  35. 101
  36. 237
  37. 279
  38. 6
  39. 27
  40. 4

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