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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 850 · 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 3 written when you write all the numbers from 1 to 80? (a) 8 (b) 19 (c) 17 (d) 18
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 4 (b) 3 (c) 5 (d) 6
  3. 3.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 2 (b) 4 (c) 3 (d) 5
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 1 (b) 4 (c) 3 (d) 2
  6. 6.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) 66 (c) 63 (d) 21
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 20 (b) 18 (c) 9 (d) 19
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 4 (b) 5 (c) 3 (d) 2
  9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 15 (b) 16 (c) 6 (d) 17
  10. 10.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 3 (d) 16
  11. 11.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 432 (c) 360 (d) 433
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 3 (b) 5 (c) 2 (d) 4
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 2 (b) 5 (c) 3 (d) 4
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 6 (b) 7 (c) 5 (d) 4
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 19 (b) 9 (c) 18 (d) 20
  16. 16.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) 36 (b) 11 (c) 33 (d) 99
  17. 17.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 309 (b) 318 (c) 319 (d) 284
  18. 18.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 331 (b) 330 (c) 321 (d) 292
  19. 19.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  20. 20.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) 207 (c) 69 (d) 72
  21. 21.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 4 (b) 2 (c) 3 (d) 1
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 15 (b) 14 (c) 4 (d) 13
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 17 (b) 16 (c) 6 (d) 18
  25. 25.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 456 (c) 577 (d) 567
  26. 26.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) 12 (b) 39 (c) 36 (d) 108
  27. 27.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
  28. 28.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) 57 (c) 60 (d) 171
  29. 29.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 24 (c) 63 (d) 7
  30. 30.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 296 (c) 327 (d) 337
  31. 31.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 46 (c) 56 (d) 55
  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) 69 (b) 198 (c) 66 (d) 22
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 7 (b) 18 (c) 17 (d) 16
  34. 34.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 428 (b) 534 (c) 525 (d) 535
  35. 35.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 405 (c) 396 (d) 406
  36. 36.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 600 (b) 609 (c) 478 (d) 610
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 2 (b) 4 (c) 5 (d) 3
  38. 38.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 585 (c) 595 (d) 594
  39. 39.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 8 (d) 7
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 7 (b) 18 (c) 17 (d) 16

Answer key

  1. 18
  2. 5
  3. 4
  4. 4
  5. 3
  6. 63
  7. 19
  8. 4
  9. 16
  10. 4
  11. 432
  12. 4
  13. 4
  14. 6
  15. 19
  16. 33
  17. 318
  18. 330
  19. 2
  20. 69
  21. 5
  22. 3
  23. 14
  24. 17
  25. 576
  26. 36
  27. 42
  28. 57
  29. 21
  30. 336
  31. 55
  32. 66
  33. 17
  34. 534
  35. 405
  36. 609
  37. 4
  38. 594
  39. 7
  40. 17

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