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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 431 · 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 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 483 (c) 484 (d) 474
  2. 2.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) 16 (b) 48 (c) 144 (d) 51
  3. 3.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) 162 (b) 18 (c) 54 (d) 57
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 8 (b) 19 (c) 18 (d) 20
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 12 (b) 10 (c) 13 (d) 9
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 6 (b) 15 (c) 17 (d) 16
  7. 7.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 484 (c) 619 (d) 618
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 12 (b) 14 (c) 3 (d) 13
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 14 (b) 16 (c) 15 (d) 4
  10. 10.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) 39 (c) 13 (d) 42
  11. 11.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  12. 12.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) 72 (b) 75 (c) 24 (d) 216
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 17 (b) 19 (c) 18 (d) 7
  14. 14.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 421 (c) 352 (d) 411
  15. 15.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 16 (d) 3
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 16 (b) 18 (c) 7 (d) 17
  17. 17.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 9 (b) 20 (c) 19 (d) 18
  19. 19.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) 54 (b) 18 (c) 6 (d) 21
  20. 20.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
  21. 21.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) 66 (b) 21 (c) 189 (d) 63
  22. 22.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 8 (d) 10
  23. 23.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 6 (b) 7 (c) 4 (d) 5
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 4 (b) 6 (c) 3 (d) 5
  26. 26.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) 57 (b) 171 (c) 19 (d) 60
  27. 27.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 78 (c) 77 (d) 68
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 78? (a) 17 (b) 19 (c) 7 (d) 18
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 12 (b) 9 (c) 11 (d) 6
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 21 (b) 9 (c) 19 (d) 20
  31. 31.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 267 (c) 250 (d) 258
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 14 (b) 15 (c) 13 (d) 3
  33. 33.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 45 (c) 5 (d) 18
  34. 34.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 111 (c) 112 (d) 120
  35. 35.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) 72 (b) 69 (c) 23 (d) 207
  36. 36.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 68? (a) 6 (b) 7 (c) 5 (d) 8
  38. 38.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 210 (c) 218 (d) 220
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 2 (b) 3 (c) 4 (d) 1
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 56? (a) 3 (b) 6 (c) 5 (d) 4

Answer key

  1. 483
  2. 48
  3. 54
  4. 19
  5. 12
  6. 16
  7. 618
  8. 13
  9. 15
  10. 39
  11. 3
  12. 72
  13. 18
  14. 420
  15. 4
  16. 17
  17. 2
  18. 19
  19. 18
  20. 6
  21. 63
  22. 7
  23. 2
  24. 6
  25. 5
  26. 57
  27. 77
  28. 18
  29. 11
  30. 20
  31. 267
  32. 14
  33. 15
  34. 111
  35. 69
  36. 5
  37. 7
  38. 219
  39. 3
  40. 5

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