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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 296 · 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 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) 7 (c) 63 (d) 24
  2. 2.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) 72 (c) 69 (d) 207
  3. 3.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  4. 4.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
  5. 5.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
  6. 6.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) 20 (b) 180 (c) 60 (d) 63
  7. 7.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 152 (c) 161 (d) 170
  8. 8.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) 90 (d) 30
  9. 9.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 7 (d) 5
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 7 (b) 5 (c) 9 (d) 10
  11. 11.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 181 (b) 182 (c) 190 (d) 172
  12. 12.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 14 (b) 7 (c) 15 (d) 12
  14. 14.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  15. 15.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) 22 (b) 66 (c) 198 (d) 69
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 14 (b) 16 (c) 4 (d) 15
  17. 17.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 8 (d) 13
  18. 18.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) 18 (b) 162 (c) 54 (d) 57
  19. 19.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  20. 20.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) 48 (c) 45 (d) 15
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 81? (a) 17 (b) 8 (c) 19 (d) 18
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 18 (b) 16 (c) 7 (d) 17
  23. 23.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 403 (b) 402 (c) 340 (d) 393
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 54? (a) 16 (b) 5 (c) 17 (d) 15
  25. 25.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) 126 (c) 42 (d) 14
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 6 (b) 18 (c) 16 (d) 17
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 60? (a) 15 (b) 16 (c) 17 (d) 6
  28. 28.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 71 (b) 62 (c) 72 (d) 80
  29. 29.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) 27 (b) 9 (c) 81 (d) 30
  30. 30.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) 144 (d) 51
  31. 31.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 5 (d) 16
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 53? (a) 16 (b) 17 (c) 15 (d) 5
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 9 (b) 11 (c) 4 (d) 10
  34. 34.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) 381 (c) 382 (d) 326
  35. 35.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 13 (b) 15 (c) 14 (d) 3
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 14 (b) 16 (c) 4 (d) 15
  38. 38.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  39. 39.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 433 (b) 432 (c) 423 (d) 360
  40. 40.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 349 (b) 304 (c) 348 (d) 339

Answer key

  1. 21
  2. 69
  3. 6
  4. 15
  5. 8
  6. 60
  7. 161
  8. 30
  9. 6
  10. 9
  11. 181
  12. 3
  13. 14
  14. 5
  15. 66
  16. 15
  17. 7
  18. 54
  19. 2
  20. 45
  21. 18
  22. 17
  23. 402
  24. 16
  25. 42
  26. 17
  27. 16
  28. 71
  29. 27
  30. 48
  31. 4
  32. 16
  33. 10
  34. 381
  35. 9
  36. 14
  37. 15
  38. 3
  39. 432
  40. 348

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