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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 746 · 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 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 302 (b) 346 (c) 345 (d) 336
  2. 2.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 475 (b) 474 (c) 388 (d) 465
  3. 3.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
  4. 4.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 230 (b) 228 (c) 238 (d) 237
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 16 (b) 15 (c) 14 (d) 4
  6. 6.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 95 (b) 104 (c) 86 (d) 96
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 3 (b) 2 (c) 4 (d) 5
  8. 8.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) 51 (b) 16 (c) 48 (d) 144
  9. 9.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 12 (d) 9
  10. 10.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 26 (c) 44 (d) 35
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 7 (b) 8 (c) 5 (d) 6
  12. 12.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 199 (c) 204 (d) 198
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  14. 14.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 340 (b) 402 (c) 403 (d) 393
  15. 15.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 486 (c) 495 (d) 496
  16. 16.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) 69 (c) 207 (d) 72
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 79? (a) 9 (b) 8 (c) 6 (d) 7
  18. 18.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) 33 (d) 36
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 5 (b) 4 (c) 3 (d) 2
  20. 20.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) 72 (b) 75 (c) 216 (d) 24
  21. 21.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 179 (b) 170 (c) 180 (d) 188
  22. 22.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 18 (c) 15 (d) 45
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 72? (a) 11 (b) 8 (c) 7 (d) 10
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 7 (b) 19 (c) 18 (d) 17
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 6 (b) 18 (c) 17 (d) 16
  26. 26.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) 19 (b) 60 (c) 57 (d) 171
  27. 27.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 155 (b) 164 (c) 156 (d) 146
  28. 28.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  29. 29.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) 135 (b) 48 (c) 45 (d) 15
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 17 (b) 19 (c) 18 (d) 7
  31. 31.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 131 (b) 122 (c) 140 (d) 132
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 4 (b) 5 (c) 2 (d) 3
  33. 33.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
  34. 34.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 168 (c) 177 (d) 186
  35. 35.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  36. 36.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 226 (c) 216 (d) 225
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 78? (a) 19 (b) 18 (c) 7 (d) 17
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 18 (b) 6 (c) 16 (d) 17
  39. 39.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 5 (b) 17 (c) 16 (d) 15

Answer key

  1. 345
  2. 474
  3. 4
  4. 237
  5. 15
  6. 95
  7. 4
  8. 48
  9. 8
  10. 35
  11. 7
  12. 198
  13. 8
  14. 402
  15. 495
  16. 69
  17. 8
  18. 33
  19. 4
  20. 72
  21. 179
  22. 15
  23. 10
  24. 18
  25. 17
  26. 57
  27. 155
  28. 3
  29. 45
  30. 18
  31. 131
  32. 4
  33. 5
  34. 177
  35. 2
  36. 225
  37. 18
  38. 17
  39. 7
  40. 16

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