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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 70 · 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 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 194 (b) 185 (c) 176 (d) 186
  2. 2.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 17 (b) 16 (c) 15 (d) 5
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 6 (b) 3 (c) 5 (d) 4
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 13 (b) 14 (c) 12 (d) 3
  7. 7.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) 6 (b) 54 (c) 18 (d) 21
  8. 8.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) 180 (c) 20 (d) 60
  9. 9.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) 45 (b) 135 (c) 15 (d) 48
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 20 (b) 18 (c) 19 (d) 8
  11. 11.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  12. 12.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) 66 (b) 198 (c) 22 (d) 69
  13. 13.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
  14. 14.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 53 (c) 44 (d) 62
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 3 (b) 2 (c) 4 (d) 1
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 8 (b) 18 (c) 20 (d) 19
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 9 (b) 19 (c) 18 (d) 20
  18. 18.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) 171 (b) 19 (c) 57 (d) 60
  19. 19.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) 48 (c) 16 (d) 144
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 5 (b) 4 (c) 2 (d) 3
  21. 21.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 438 (c) 370 (d) 447
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 13 (b) 14 (c) 15 (d) 3
  23. 23.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 462 (c) 585 (d) 586
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 4 (b) 3 (c) 6 (d) 5
  25. 25.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 468 (c) 585 (d) 595
  26. 26.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  27. 27.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 83 (c) 74 (d) 84
  28. 28.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  29. 29.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 131 (c) 140 (d) 132
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 3 (b) 1 (c) 2 (d) 4
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 17 (b) 18 (c) 8 (d) 19
  32. 32.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 525 (b) 516 (c) 422 (d) 526
  33. 33.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) 33 (b) 30 (c) 10 (d) 90
  34. 34.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 223 (c) 222 (d) 213
  35. 35.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  36. 36.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) 13 (b) 117 (c) 39 (d) 42
  37. 37.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  38. 38.The numbers 4 to 12 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) 8 (c) 24 (d) 27
  39. 39.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 489 (c) 398 (d) 480
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 3 (b) 4 (c) 5 (d) 6

Answer key

  1. 185
  2. 2
  3. 5
  4. 16
  5. 5
  6. 13
  7. 18
  8. 60
  9. 45
  10. 19
  11. 9
  12. 66
  13. 6
  14. 53
  15. 3
  16. 19
  17. 19
  18. 57
  19. 48
  20. 4
  21. 447
  22. 14
  23. 585
  24. 5
  25. 594
  26. 9
  27. 83
  28. 4
  29. 131
  30. 3
  31. 18
  32. 525
  33. 30
  34. 222
  35. 7
  36. 39
  37. 5
  38. 24
  39. 489
  40. 5

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