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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 229 · 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 9? (a) 9 (b) 10 (c) 8 (d) 11
  2. 2.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 7 (b) 5 (c) 6 (d) 4
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 7 (b) 19 (c) 17 (d) 18
  5. 5.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 182 (c) 164 (d) 173
  6. 6.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  7. 7.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 7 (b) 16 (c) 18 (d) 17
  9. 9.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  10. 10.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) 7 (c) 24 (d) 21
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 3 (b) 1 (c) 4 (d) 2
  12. 12.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 114 (c) 123 (d) 124
  13. 13.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 150 (c) 159 (d) 160
  14. 14.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 267 (c) 276 (d) 277
  15. 15.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  16. 16.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) 24 (b) 75 (c) 72 (d) 216
  17. 17.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 496 (c) 402 (d) 495
  18. 18.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) 45 (b) 14 (c) 126 (d) 42
  19. 19.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 543 (c) 440 (d) 553
  20. 20.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
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 16 (b) 7 (c) 18 (d) 17
  22. 22.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 10 (b) 90 (c) 33 (d) 30
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 70? (a) 18 (b) 17 (c) 16 (d) 7
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 4 (b) 3 (c) 1 (d) 2
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 7 (b) 5 (c) 6 (d) 8
  26. 26.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 12 (d) 9
  27. 27.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) 33 (c) 11 (d) 99
  28. 28.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 4 (b) 3 (c) 2 (d) 1
  30. 30.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) 21 (b) 189 (c) 66 (d) 63
  31. 31.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 15 (b) 4 (c) 14 (d) 16
  33. 33.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  34. 34.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) 20 (b) 63 (c) 60 (d) 180
  35. 35.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
  36. 36.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) 69 (b) 22 (c) 66 (d) 198
  37. 37.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) 72 (b) 24 (c) 8 (d) 27
  38. 38.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 4 (d) 15
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 62? (a) 6 (b) 17 (c) 15 (d) 16
  40. 40.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 137 (c) 128 (d) 146

Answer key

  1. 9
  2. 6
  3. 6
  4. 18
  5. 173
  6. 4
  7. 6
  8. 17
  9. 2
  10. 21
  11. 3
  12. 123
  13. 159
  14. 276
  15. 2
  16. 72
  17. 495
  18. 42
  19. 552
  20. 48
  21. 17
  22. 30
  23. 17
  24. 3
  25. 7
  26. 8
  27. 33
  28. 9
  29. 3
  30. 63
  31. 7
  32. 15
  33. 3
  34. 60
  35. 57
  36. 66
  37. 24
  38. 5
  39. 16
  40. 137

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