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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 673 · 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 times is the digit 6 written when you write all the numbers from 1 to 53? (a) 6 (b) 3 (c) 4 (d) 5
  2. 2.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
  3. 3.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 415 (c) 405 (d) 348
  4. 4.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
  5. 5.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 220 (c) 223 (d) 213
  6. 6.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 3 (d) 1
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 7 (b) 4 (c) 5 (d) 6
  8. 8.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
  9. 9.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 586 (c) 576 (d) 585
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 9 (b) 19 (c) 21 (d) 20
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  13. 13.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) 21 (c) 189 (d) 63
  14. 14.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 17 (b) 5 (c) 15 (d) 16
  16. 16.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 151 (c) 152 (d) 160
  17. 17.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 92 (c) 100 (d) 91
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 15 (b) 17 (c) 16 (d) 5
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 42? (a) 3 (b) 2 (c) 5 (d) 4
  20. 20.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) 54 (b) 6 (c) 21 (d) 18
  21. 21.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) 60 (c) 20 (d) 63
  22. 22.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  23. 23.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
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 21 (b) 9 (c) 19 (d) 20
  25. 25.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 446 (c) 562 (d) 561
  26. 26.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) 16 (b) 51 (c) 144 (d) 48
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 1 (b) 3 (c) 2 (d) 4
  28. 28.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 4 (d) 6
  29. 29.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
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 95? (a) 19 (b) 9 (c) 20 (d) 18
  31. 31.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
  32. 32.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) 198 (b) 66 (c) 22 (d) 69
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 2 (b) 4 (c) 5 (d) 3
  34. 34.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 7 (b) 8 (c) 9 (d) 10
  36. 36.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) 188 (c) 180 (d) 179
  37. 37.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 110 (c) 119 (d) 120
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 5 (d) 4
  39. 39.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 176 (c) 158 (d) 167
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 17 (b) 7 (c) 16 (d) 18

Answer key

  1. 5
  2. 24
  3. 414
  4. 42
  5. 222
  6. 2
  7. 6
  8. 43
  9. 585
  10. 7
  11. 20
  12. 9
  13. 63
  14. 7
  15. 16
  16. 151
  17. 91
  18. 16
  19. 4
  20. 18
  21. 60
  22. 4
  23. 36
  24. 20
  25. 561
  26. 48
  27. 3
  28. 5
  29. 69
  30. 19
  31. 5
  32. 66
  33. 4
  34. 3
  35. 9
  36. 179
  37. 119
  38. 5
  39. 167
  40. 17

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