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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 511 · 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.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 345 (c) 355 (d) 308
  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) 81 (c) 27 (d) 30
  3. 3.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) 39 (b) 42 (c) 13 (d) 117
  4. 4.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  5. 5.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) 20 (c) 180 (d) 63
  6. 6.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) 144 (b) 51 (c) 48 (d) 16
  7. 7.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 603 (c) 612 (d) 613
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 3 (b) 12 (c) 13 (d) 14
  9. 9.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  10. 10.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) 19 (d) 60
  11. 11.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) 42 (b) 126 (c) 14 (d) 45
  12. 12.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) 21 (d) 54
  13. 13.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) 11 (c) 33 (d) 99
  14. 14.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 126 (c) 136 (d) 135
  15. 15.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) 75 (b) 72 (c) 216 (d) 24
  16. 16.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 441 (c) 432 (d) 366
  17. 17.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  18. 18.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 595 (c) 468 (d) 594
  19. 19.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  20. 20.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 52 (c) 43 (d) 44
  21. 21.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) 15 (d) 45
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 6 (b) 3 (c) 4 (d) 5
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 85? (a) 19 (b) 18 (c) 8 (d) 20
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 70? (a) 6 (b) 8 (c) 5 (d) 7
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 14 (b) 16 (c) 15 (d) 5
  26. 26.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 69 (b) 60 (c) 70 (d) 78
  27. 27.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 540 (b) 550 (c) 549 (d) 438
  28. 28.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 16 (b) 17 (c) 7 (d) 18
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 2 (d) 3
  31. 31.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) 39 (c) 108 (d) 12
  32. 32.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 87? (a) 14 (b) 16 (c) 8 (d) 17
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 3 (b) 1 (c) 4 (d) 2
  35. 35.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  36. 36.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) 24 (b) 7 (c) 63 (d) 21
  37. 37.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  38. 38.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
  39. 39.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) 18 (c) 57 (d) 54
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 19 (b) 18 (c) 8 (d) 17

Answer key

  1. 354
  2. 27
  3. 39
  4. 7
  5. 60
  6. 48
  7. 612
  8. 13
  9. 4
  10. 57
  11. 42
  12. 18
  13. 33
  14. 135
  15. 72
  16. 441
  17. 3
  18. 594
  19. 4
  20. 43
  21. 45
  22. 5
  23. 19
  24. 7
  25. 15
  26. 69
  27. 549
  28. 9
  29. 17
  30. 3
  31. 36
  32. 7
  33. 16
  34. 3
  35. 5
  36. 21
  37. 2
  38. 69
  39. 54
  40. 18

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