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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 544 · 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 two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
  2. 2.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) 9 (b) 30 (c) 27 (d) 81
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 6 (b) 5 (c) 4 (d) 7
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 18 (d) 19
  5. 5.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
  6. 6.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) 39 (d) 108
  7. 7.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  8. 8.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
  9. 9.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) 63 (b) 20 (c) 60 (d) 180
  10. 10.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) 72 (b) 23 (c) 207 (d) 69
  11. 11.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 609 (c) 600 (d) 478
  12. 12.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 86 (c) 96 (d) 95
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 92? (a) 19 (b) 9 (c) 21 (d) 20
  14. 14.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 6 (d) 15
  15. 15.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) 24 (d) 7
  16. 16.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 3 (d) 1
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 13 (b) 12 (c) 11 (d) 3
  18. 18.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 588 (b) 464 (c) 579 (d) 589
  19. 19.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 482 (c) 616 (d) 615
  20. 20.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 99 (b) 108 (c) 100 (d) 90
  21. 21.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 565 (b) 555 (c) 448 (d) 564
  22. 22.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 290 (c) 328 (d) 318
  23. 23.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
  24. 24.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) 99 (b) 36 (c) 11 (d) 33
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 6 (b) 16 (c) 17 (d) 18
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 3 (b) 5 (c) 2 (d) 4
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 17 (b) 19 (c) 8 (d) 18
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 9 (b) 12 (c) 11 (d) 8
  29. 29.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  30. 30.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 39 (c) 13 (d) 42
  31. 31.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 238 (c) 240 (d) 249
  32. 32.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 5 (d) 3
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 5 (b) 3 (c) 2 (d) 4
  34. 34.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) 172 (c) 182 (d) 190
  35. 35.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) 51 (b) 153 (c) 17 (d) 54
  36. 36.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 76 (c) 58 (d) 67
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 2 (b) 4 (c) 5 (d) 3
  38. 38.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 501 (c) 406 (d) 502
  39. 39.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) 6 (c) 54 (d) 21
  40. 40.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7

Answer key

  1. 3
  2. 27
  3. 6
  4. 19
  5. 3
  6. 36
  7. 5
  8. 8
  9. 60
  10. 69
  11. 609
  12. 95
  13. 20
  14. 5
  15. 21
  16. 2
  17. 12
  18. 588
  19. 615
  20. 99
  21. 564
  22. 327
  23. 54
  24. 33
  25. 17
  26. 4
  27. 18
  28. 11
  29. 4
  30. 39
  31. 249
  32. 4
  33. 4
  34. 181
  35. 51
  36. 67
  37. 4
  38. 501
  39. 18
  40. 8

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