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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 546 · 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 7? (a) 6 (b) 7 (c) 8 (d) 10
  2. 2.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) 45 (b) 15 (c) 48 (d) 135
  3. 3.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
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 6 (b) 4 (c) 5 (d) 3
  5. 5.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
  6. 6.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  7. 7.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 501 (b) 502 (c) 406 (d) 492
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 19 (b) 21 (c) 20 (d) 9
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 9 (b) 20 (c) 21 (d) 19
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
  11. 11.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 8 (d) 13
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
  13. 13.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) 63 (b) 24 (c) 7 (d) 21
  14. 14.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) 66 (b) 189 (c) 63 (d) 21
  15. 15.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) 17 (b) 153 (c) 54 (d) 51
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 94? (a) 19 (b) 9 (c) 21 (d) 20
  17. 17.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 104 (c) 103 (d) 94
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 17 (b) 18 (c) 8 (d) 19
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 86? (a) 8 (b) 19 (c) 18 (d) 20
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 4 (b) 2 (c) 3 (d) 5
  21. 21.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) 57 (c) 171 (d) 19
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 17 (b) 19 (c) 7 (d) 18
  23. 23.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6
  24. 24.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 179 (c) 180 (d) 188
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 20 (b) 8 (c) 18 (d) 19
  26. 26.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 613 (b) 612 (c) 480 (d) 603
  27. 27.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 5 (d) 10
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 9 (b) 20 (c) 19 (d) 21
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 2 (b) 4 (c) 3 (d) 5
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 6 (b) 11 (c) 9 (d) 12
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 15 (b) 14 (c) 16 (d) 5
  32. 32.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 2 (d) 4
  33. 33.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) 24 (b) 27 (c) 72 (d) 8
  34. 34.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
  35. 35.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 11 (b) 14 (c) 13 (d) 8
  37. 37.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) 30 (d) 27
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 19 (b) 8 (c) 20 (d) 18
  39. 39.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 114 (c) 132 (d) 123
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 7 (b) 18 (c) 16 (d) 17

Answer key

  1. 7
  2. 45
  3. 18
  4. 5
  5. 5
  6. 2
  7. 501
  8. 20
  9. 20
  10. 3
  11. 7
  12. 9
  13. 21
  14. 63
  15. 51
  16. 20
  17. 103
  18. 18
  19. 19
  20. 4
  21. 57
  22. 18
  23. 6
  24. 179
  25. 19
  26. 612
  27. 4
  28. 20
  29. 4
  30. 11
  31. 15
  32. 3
  33. 24
  34. 8
  35. 6
  36. 13
  37. 27
  38. 19
  39. 123
  40. 17

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