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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 417 · 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 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 571 (b) 570 (c) 561 (d) 452
  2. 2.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) 15 (b) 5 (c) 18 (d) 45
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 16 (b) 18 (c) 6 (d) 17
  4. 4.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 492 (c) 493 (d) 400
  5. 5.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 95 (b) 96 (c) 104 (d) 86
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 98? (a) 21 (b) 20 (c) 19 (d) 9
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 1 (b) 4 (c) 2 (d) 3
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 38? (a) 2 (b) 5 (c) 3 (d) 4
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 9 (d) 19
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 16 (b) 17 (c) 7 (d) 18
  11. 11.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 3 (b) 15 (c) 14 (d) 13
  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) 99 (b) 11 (c) 36 (d) 33
  14. 14.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 184 (c) 175 (d) 176
  15. 15.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) 14 (b) 42 (c) 126 (d) 45
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 5 (b) 17 (c) 15 (d) 16
  17. 17.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  18. 18.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 16 (d) 3
  19. 19.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) 69 (c) 198 (d) 66
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 5 (b) 4 (c) 2 (d) 3
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 7 (b) 18 (c) 19 (d) 17
  22. 22.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) 153 (c) 17 (d) 51
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 19 (b) 21 (c) 20 (d) 9
  24. 24.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
  25. 25.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 5 (b) 2 (c) 3 (d) 4
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 72? (a) 8 (b) 10 (c) 7 (d) 11
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 21 (b) 19 (c) 20 (d) 9
  29. 29.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 552 (c) 440 (d) 553
  30. 30.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) 81 (b) 9 (c) 30 (d) 27
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 4 (b) 5 (c) 3 (d) 2
  32. 32.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 480 (c) 398 (d) 490
  33. 33.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
  34. 34.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) 8 (b) 27 (c) 72 (d) 24
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 19 (d) 21
  36. 36.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 18 (b) 7 (c) 16 (d) 17
  38. 38.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 9 (d) 10
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 18 (b) 17 (c) 8 (d) 19
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 18 (b) 19 (c) 8 (d) 20

Answer key

  1. 570
  2. 15
  3. 17
  4. 492
  5. 95
  6. 20
  7. 3
  8. 4
  9. 19
  10. 17
  11. 2
  12. 14
  13. 33
  14. 175
  15. 42
  16. 16
  17. 6
  18. 4
  19. 66
  20. 4
  21. 18
  22. 51
  23. 20
  24. 7
  25. 5
  26. 4
  27. 10
  28. 20
  29. 552
  30. 27
  31. 4
  32. 489
  33. 7
  34. 24
  35. 20
  36. 9
  37. 17
  38. 9
  39. 18
  40. 19

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