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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 716 · 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 6 written when you write all the numbers from 1 to 86? (a) 18 (b) 8 (c) 19 (d) 20
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 8 (b) 7 (c) 5 (d) 6
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 8 (b) 18 (c) 19 (d) 20
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 89? (a) 18 (b) 19 (c) 8 (d) 20
  5. 5.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) 63 (b) 20 (c) 60 (d) 180
  6. 6.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 5 (d) 3
  8. 8.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 6 (c) 21 (d) 54
  9. 9.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 379 (b) 369 (c) 378 (d) 324
  10. 10.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) 45 (b) 126 (c) 42 (d) 14
  11. 11.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 370 (c) 448 (d) 447
  12. 12.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 272 (b) 301 (c) 300 (d) 291
  13. 13.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 8 (d) 11
  14. 14.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 438 (c) 439 (d) 429
  15. 15.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 54 (c) 46 (d) 45
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 3 (b) 13 (c) 15 (d) 14
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 8 (b) 17 (c) 18 (d) 19
  18. 18.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 403 (b) 402 (c) 393 (d) 340
  19. 19.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  20. 20.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  21. 21.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) 75 (b) 24 (c) 216 (d) 72
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 6 (b) 4 (c) 5 (d) 7
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 97? (a) 9 (b) 20 (c) 21 (d) 19
  24. 24.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  25. 25.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 7 (d) 8
  26. 26.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 451 (c) 450 (d) 372
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 17 (b) 16 (c) 18 (d) 6
  28. 28.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 474 (c) 604 (d) 603
  29. 29.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 86 (c) 77 (d) 68
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 73? (a) 16 (b) 7 (c) 17 (d) 18
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 19 (b) 17 (c) 8 (d) 18
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 7 (b) 17 (c) 18 (d) 19
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 5 (b) 15 (c) 17 (d) 16
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 9 (b) 19 (c) 20 (d) 21
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 43? (a) 4 (b) 2 (c) 5 (d) 3
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 19 (b) 20 (c) 21 (d) 9
  37. 37.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) 144 (b) 48 (c) 16 (d) 51
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 64? (a) 16 (b) 6 (c) 18 (d) 17
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 4 (b) 5 (c) 2 (d) 3
  40. 40.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) 22 (d) 66

Answer key

  1. 19
  2. 7
  3. 19
  4. 19
  5. 60
  6. 8
  7. 4
  8. 18
  9. 378
  10. 42
  11. 447
  12. 300
  13. 9
  14. 438
  15. 45
  16. 14
  17. 18
  18. 402
  19. 4
  20. 3
  21. 72
  22. 6
  23. 20
  24. 5
  25. 7
  26. 450
  27. 17
  28. 603
  29. 77
  30. 17
  31. 18
  32. 18
  33. 16
  34. 20
  35. 4
  36. 20
  37. 48
  38. 17
  39. 4
  40. 66

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