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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 907 · 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.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) 48 (b) 51 (c) 144 (d) 16
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 14 (b) 15 (c) 13 (d) 4
  3. 3.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  4. 4.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  5. 5.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 390 (c) 399 (d) 338
  6. 6.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  7. 7.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 163 (b) 172 (c) 164 (d) 154
  8. 8.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 8 (d) 6
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 62? (a) 5 (b) 4 (c) 6 (d) 7
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 8 (b) 20 (c) 18 (d) 19
  11. 11.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 330 (c) 388 (d) 387
  12. 12.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 17 (b) 15 (c) 5 (d) 16
  14. 14.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
  15. 15.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) 90 (b) 33 (c) 10 (d) 30
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 9 (b) 19 (c) 21 (d) 20
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 52? (a) 5 (b) 6 (c) 4 (d) 3
  18. 18.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  19. 19.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 266 (c) 291 (d) 282
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  21. 21.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 59 (c) 50 (d) 60
  22. 22.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  23. 23.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 117 (c) 39 (d) 42
  24. 24.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) 123 (c) 114 (d) 132
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 5 (b) 6 (c) 4 (d) 7
  26. 26.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  27. 27.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) 6 (b) 54 (c) 21 (d) 18
  28. 28.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 193 (b) 200 (c) 183 (d) 192
  29. 29.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) 66 (c) 22 (d) 198
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 3 (b) 4 (c) 6 (d) 5
  31. 31.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 152 (c) 134 (d) 143
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 56? (a) 16 (b) 5 (c) 17 (d) 15
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 14 (b) 15 (c) 16 (d) 4
  34. 34.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 235 (c) 228 (d) 225
  35. 35.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
  36. 36.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  37. 37.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 120 (c) 129 (d) 138
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 7 (b) 18 (c) 17 (d) 19
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 2 (b) 3 (c) 1 (d) 4
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 73? (a) 11 (b) 7 (c) 12 (d) 9

Answer key

  1. 48
  2. 14
  3. 8
  4. 9
  5. 399
  6. 5
  7. 163
  8. 7
  9. 6
  10. 19
  11. 387
  12. 4
  13. 16
  14. 585
  15. 30
  16. 20
  17. 5
  18. 8
  19. 291
  20. 4
  21. 59
  22. 6
  23. 39
  24. 123
  25. 6
  26. 3
  27. 18
  28. 192
  29. 66
  30. 5
  31. 143
  32. 16
  33. 15
  34. 234
  35. 33
  36. 7
  37. 129
  38. 18
  39. 3
  40. 11

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