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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 28 · 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 15? (a) 5 (b) 16 (c) 4 (d) 3
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 5 (b) 3 (c) 4 (d) 2
  3. 3.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) 24 (d) 63
  4. 4.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
  5. 5.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) 72 (b) 75 (c) 216 (d) 24
  6. 6.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) 69 (c) 66 (d) 22
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 15 (b) 13 (c) 3 (d) 14
  8. 8.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 496 (b) 402 (c) 495 (d) 486
  9. 9.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
  10. 10.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 10 (d) 1
  11. 11.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 4 (d) 10
  12. 12.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 42 (c) 41 (d) 50
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 6 (b) 18 (c) 16 (d) 17
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 68? (a) 15 (b) 17 (c) 6 (d) 16
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 4 (b) 15 (c) 16 (d) 14
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 19 (b) 7 (c) 18 (d) 17
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 17 (b) 5 (c) 15 (d) 16
  18. 18.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 7 (b) 19 (c) 17 (d) 18
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 96? (a) 9 (b) 19 (c) 20 (d) 21
  21. 21.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  22. 22.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 483 (c) 474 (d) 484
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 3 (b) 14 (c) 15 (d) 13
  24. 24.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 76 (c) 84 (d) 75
  25. 25.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 10 (d) 5
  26. 26.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) 207 (c) 23 (d) 69
  27. 27.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) 21 (b) 6 (c) 18 (d) 54
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 11 (b) 8 (c) 5 (d) 10
  29. 29.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) 126 (b) 45 (c) 14 (d) 42
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 4 (b) 16 (c) 15 (d) 14
  31. 31.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 15 (d) 4
  32. 32.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 391 (b) 381 (c) 390 (d) 332
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 17 (b) 18 (c) 19 (d) 8
  34. 34.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
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 14 (b) 5 (c) 16 (d) 15
  36. 36.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 37 (b) 46 (c) 38 (d) 28
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 3 (b) 1 (c) 2 (d) 4
  38. 38.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) 60 (b) 19 (c) 57 (d) 171
  39. 39.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 180 (c) 171 (d) 172
  40. 40.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 340 (b) 339 (c) 298 (d) 330

Answer key

  1. 4
  2. 4
  3. 21
  4. 51
  5. 72
  6. 66
  7. 14
  8. 495
  9. 3
  10. 2
  11. 3
  12. 41
  13. 17
  14. 16
  15. 15
  16. 18
  17. 16
  18. 7
  19. 18
  20. 20
  21. 9
  22. 483
  23. 14
  24. 75
  25. 6
  26. 69
  27. 18
  28. 10
  29. 42
  30. 15
  31. 5
  32. 390
  33. 18
  34. 63
  35. 15
  36. 37
  37. 3
  38. 57
  39. 171
  40. 339

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