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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 630 · 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 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 418 (c) 417 (d) 350
  2. 2.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 9 (d) 12
  3. 3.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  4. 4.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 80? (a) 17 (b) 8 (c) 18 (d) 19
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 86? (a) 7 (b) 8 (c) 9 (d) 6
  7. 7.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
  8. 8.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) 91 (d) 100
  9. 9.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 375 (c) 376 (d) 366
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 18 (b) 6 (c) 16 (d) 17
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 73? (a) 17 (b) 7 (c) 16 (d) 18
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 7 (b) 17 (c) 18 (d) 19
  13. 13.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 17 (b) 16 (c) 6 (d) 18
  15. 15.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) 72 (b) 69 (c) 207 (d) 23
  16. 16.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  17. 17.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) 10 (c) 33 (d) 30
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 6 (b) 4 (c) 5 (d) 3
  19. 19.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 135 (c) 126 (d) 136
  20. 20.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  21. 21.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 336 (c) 345 (d) 302
  22. 22.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 162 (c) 54 (d) 18
  23. 23.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 216 (c) 217 (d) 324
  24. 24.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 176 (c) 167 (d) 168
  25. 25.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) 30 (c) 27 (d) 81
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 6 (b) 5 (c) 3 (d) 4
  27. 27.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 56 (c) 65 (d) 66
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 16 (b) 18 (c) 17 (d) 6
  29. 29.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) 27 (c) 8 (d) 24
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 44? (a) 4 (b) 3 (c) 2 (d) 5
  31. 31.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 445 (b) 444 (c) 435 (d) 368
  32. 32.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  33. 33.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
  34. 34.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  35. 35.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 17 (b) 16 (c) 6 (d) 18
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 2 (b) 5 (c) 4 (d) 3
  38. 38.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  39. 39.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) 63 (b) 21 (c) 66 (d) 189
  40. 40.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 143 (b) 152 (c) 134 (d) 144

Answer key

  1. 417
  2. 8
  3. 3
  4. 9
  5. 18
  6. 8
  7. 45
  8. 91
  9. 375
  10. 17
  11. 17
  12. 18
  13. 5
  14. 17
  15. 69
  16. 4
  17. 30
  18. 5
  19. 135
  20. 7
  21. 345
  22. 54
  23. 216
  24. 167
  25. 27
  26. 5
  27. 65
  28. 17
  29. 24
  30. 4
  31. 444
  32. 5
  33. 6
  34. 8
  35. 4
  36. 17
  37. 4
  38. 3
  39. 63
  40. 143

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