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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 863 · 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 two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 5 (d) 7
  2. 2.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  3. 3.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 16 (b) 17 (c) 15 (d) 5
  5. 5.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 108 (c) 118 (d) 117
  6. 6.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 5 (d) 4
  7. 7.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) 207 (b) 23 (c) 69 (d) 72
  8. 8.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 356 (b) 427 (c) 426 (d) 417
  9. 9.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) 63 (b) 24 (c) 7 (d) 21
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 4 (b) 3 (c) 6 (d) 5
  11. 11.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 100 (c) 109 (d) 110
  12. 12.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) 16 (c) 48 (d) 144
  13. 13.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  14. 14.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 147 (b) 156 (c) 148 (d) 138
  15. 15.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 9 (d) 10
  16. 16.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 354 (c) 424 (d) 423
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 88? (a) 18 (b) 20 (c) 19 (d) 8
  18. 18.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 6 (b) 3 (c) 4 (d) 5
  20. 20.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) 412 (c) 510 (d) 501
  21. 21.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 59 (b) 68 (c) 50 (d) 60
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 14 (b) 15 (c) 4 (d) 16
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 64? (a) 6 (b) 16 (c) 18 (d) 17
  24. 24.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 392 (b) 481 (c) 480 (d) 471
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 79? (a) 9 (b) 7 (c) 8 (d) 6
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 8 (b) 7 (c) 6 (d) 5
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 16 (b) 18 (c) 6 (d) 17
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 46? (a) 3 (b) 5 (c) 4 (d) 2
  29. 29.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 592 (b) 591 (c) 466 (d) 582
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 4 (b) 3 (c) 2 (d) 1
  31. 31.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  32. 32.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 6 (d) 4
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 6 (b) 3 (c) 5 (d) 4
  34. 34.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) 66 (c) 69 (d) 22
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 18 (b) 17 (c) 19 (d) 8
  36. 36.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 101 (b) 102 (c) 92 (d) 110
  37. 37.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  38. 38.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) 24 (c) 216 (d) 75
  39. 39.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) 5 (c) 18 (d) 45
  40. 40.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) 14 (b) 45 (c) 42 (d) 126

Answer key

  1. 6
  2. 2
  3. 3
  4. 16
  5. 117
  6. 4
  7. 69
  8. 426
  9. 21
  10. 5
  11. 109
  12. 48
  13. 4
  14. 147
  15. 9
  16. 423
  17. 19
  18. 6
  19. 5
  20. 510
  21. 59
  22. 15
  23. 17
  24. 480
  25. 8
  26. 7
  27. 17
  28. 4
  29. 591
  30. 3
  31. 8
  32. 5
  33. 5
  34. 66
  35. 18
  36. 101
  37. 5
  38. 72
  39. 15
  40. 42

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