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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 910 · 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 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 153 (b) 154 (c) 144 (d) 162
  2. 2.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 3 (b) 2 (c) 1 (d) 4
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 17 (b) 19 (c) 18 (d) 7
  5. 5.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 235 (c) 225 (d) 234
  6. 6.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  7. 7.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 54? (a) 15 (b) 17 (c) 16 (d) 5
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 21 (b) 19 (c) 20 (d) 9
  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) 60 (b) 171 (c) 57 (d) 19
  11. 11.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 24 (c) 34 (d) 33
  12. 12.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 309 (b) 318 (c) 284 (d) 319
  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) 21 (b) 24 (c) 63 (d) 7
  14. 14.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) 180 (b) 20 (c) 63 (d) 60
  15. 15.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 18 (b) 9 (c) 20 (d) 19
  17. 17.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) 72 (c) 207 (d) 69
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 6 (b) 4 (c) 5 (d) 3
  19. 19.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  20. 20.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 160 (c) 168 (d) 159
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 89? (a) 20 (b) 19 (c) 8 (d) 18
  22. 22.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 84? (a) 20 (b) 18 (c) 8 (d) 19
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 3 (b) 13 (c) 14 (d) 15
  25. 25.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 556 (c) 555 (d) 442
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 8 (b) 18 (c) 20 (d) 19
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 4 (b) 16 (c) 15 (d) 14
  28. 28.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
  29. 29.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) 39 (b) 36 (c) 12 (d) 108
  30. 30.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 4 (d) 2
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 6 (b) 16 (c) 18 (d) 17
  32. 32.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 2 (d) 1
  33. 33.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) 14 (c) 45 (d) 42
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 5 (b) 4 (c) 2 (d) 3
  35. 35.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  36. 36.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) 18 (c) 54 (d) 6
  37. 37.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 279 (c) 270 (d) 258
  38. 38.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 21 (b) 19 (c) 9 (d) 20
  40. 40.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 577 (b) 567 (c) 456 (d) 576

Answer key

  1. 153
  2. 4
  3. 3
  4. 18
  5. 234
  6. 5
  7. 9
  8. 16
  9. 20
  10. 57
  11. 33
  12. 318
  13. 21
  14. 60
  15. 4
  16. 19
  17. 69
  18. 5
  19. 8
  20. 159
  21. 19
  22. 8
  23. 19
  24. 14
  25. 555
  26. 19
  27. 15
  28. 7
  29. 36
  30. 3
  31. 17
  32. 2
  33. 42
  34. 4
  35. 3
  36. 18
  37. 279
  38. 2
  39. 20
  40. 576

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