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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 520 · 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 7 written when you write all the numbers from 1 to 82? (a) 19 (b) 18 (c) 8 (d) 17
  2. 2.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) 117 (b) 13 (c) 39 (d) 42
  3. 3.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  4. 4.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) 63 (d) 60
  5. 5.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  6. 6.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 404 (b) 499 (c) 498 (d) 489
  7. 7.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 4 (d) 2
  8. 8.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) 30 (b) 27 (c) 81 (d) 9
  9. 9.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 393 (c) 384 (d) 394
  10. 10.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 555 (c) 442 (d) 556
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 70? (a) 7 (b) 17 (c) 16 (d) 18
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 18 (b) 9 (c) 20 (d) 19
  13. 13.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 47 (b) 48 (c) 56 (d) 38
  14. 14.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
  15. 15.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 1 (d) 3
  16. 16.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 613 (b) 612 (c) 480 (d) 603
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 6 (b) 4 (c) 3 (d) 5
  18. 18.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 60 (c) 69 (d) 78
  19. 19.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 346 (c) 345 (d) 302
  20. 20.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) 144 (c) 51 (d) 16
  21. 21.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 44 (c) 54 (d) 53
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 60? (a) 6 (b) 7 (c) 8 (d) 5
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 98? (a) 9 (b) 19 (c) 20 (d) 21
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 19 (b) 18 (c) 7 (d) 17
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 54? (a) 4 (b) 5 (c) 3 (d) 6
  26. 26.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) 18 (c) 162 (d) 54
  27. 27.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 343 (b) 300 (c) 342 (d) 333
  28. 28.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 387 (c) 397 (d) 336
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 4 (b) 14 (c) 16 (d) 15
  30. 30.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) 21 (b) 189 (c) 66 (d) 63
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 18 (b) 20 (c) 9 (d) 19
  32. 32.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 316 (c) 366 (d) 367
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 2 (b) 3 (c) 1 (d) 4
  34. 34.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 42 (c) 60 (d) 51
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 3 (b) 13 (c) 14 (d) 15
  36. 36.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 4 (d) 17
  37. 37.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 421 (b) 352 (c) 411 (d) 420
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 20 (b) 18 (c) 19 (d) 8
  39. 39.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  40. 40.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 511 (b) 510 (c) 501 (d) 412

Answer key

  1. 18
  2. 39
  3. 4
  4. 60
  5. 4
  6. 498
  7. 3
  8. 27
  9. 393
  10. 555
  11. 17
  12. 19
  13. 47
  14. 5
  15. 2
  16. 612
  17. 5
  18. 69
  19. 345
  20. 48
  21. 53
  22. 7
  23. 20
  24. 18
  25. 5
  26. 54
  27. 342
  28. 396
  29. 15
  30. 63
  31. 19
  32. 366
  33. 3
  34. 51
  35. 14
  36. 3
  37. 420
  38. 19
  39. 6
  40. 510

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