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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 912 · 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 8 written when you write all the numbers from 1 to 60? (a) 5 (b) 4 (c) 7 (d) 6
  2. 2.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 2 (b) 4 (c) 3 (d) 1
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 88? (a) 19 (b) 20 (c) 8 (d) 18
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 18 (b) 19 (c) 17 (d) 7
  6. 6.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  7. 7.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) 60 (d) 63
  8. 8.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  9. 9.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) 144 (c) 16 (d) 48
  10. 10.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) 198 (c) 204 (d) 199
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 50? (a) 3 (b) 6 (c) 4 (d) 5
  12. 12.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 361 (c) 360 (d) 351
  13. 13.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 216 (c) 225 (d) 222
  14. 14.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 4 (d) 17
  15. 15.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) 189 (b) 21 (c) 66 (d) 63
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 56? (a) 6 (b) 5 (c) 3 (d) 4
  17. 17.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) 108 (b) 36 (c) 12 (d) 39
  18. 18.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) 10 (b) 90 (c) 33 (d) 30
  19. 19.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  20. 20.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 7 (d) 6
  21. 21.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 571 (c) 561 (d) 452
  22. 22.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) 57 (c) 19 (d) 171
  23. 23.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 312 (c) 313 (d) 303
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 20 (b) 19 (c) 18 (d) 8
  25. 25.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 111 (c) 112 (d) 102
  26. 26.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 4 (b) 3 (c) 5 (d) 6
  28. 28.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
  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) 198 (b) 69 (c) 66 (d) 22
  30. 30.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 433 (c) 360 (d) 423
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 5 (b) 15 (c) 17 (d) 16
  32. 32.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  33. 33.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 340 (c) 403 (d) 402
  34. 34.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) 81 (b) 9 (c) 27 (d) 30
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 1 (b) 4 (c) 2 (d) 3
  36. 36.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 290 (c) 328 (d) 318
  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) 120 (b) 110 (c) 119 (d) 128
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 73? (a) 7 (b) 5 (c) 8 (d) 6
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 45? (a) 4 (b) 3 (c) 5 (d) 6
  40. 40.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 502 (b) 406 (c) 492 (d) 501

Answer key

  1. 6
  2. 4
  3. 3
  4. 19
  5. 18
  6. 5
  7. 60
  8. 6
  9. 48
  10. 198
  11. 5
  12. 360
  13. 225
  14. 3
  15. 63
  16. 5
  17. 36
  18. 30
  19. 2
  20. 7
  21. 570
  22. 57
  23. 312
  24. 19
  25. 111
  26. 8
  27. 5
  28. 9
  29. 66
  30. 432
  31. 16
  32. 5
  33. 402
  34. 27
  35. 3
  36. 327
  37. 119
  38. 7
  39. 5
  40. 501

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