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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 692 · 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 5? (a) 10 (b) 5 (c) 4 (d) 6
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 18 (b) 7 (c) 19 (d) 17
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 84? (a) 19 (b) 20 (c) 8 (d) 18
  4. 4.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 15 (d) 16
  6. 6.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  7. 7.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) 126 (c) 42 (d) 45
  8. 8.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) 16 (c) 144 (d) 51
  9. 9.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 110 (c) 109 (d) 118
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 94? (a) 19 (b) 18 (c) 20 (d) 9
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 5 (b) 3 (c) 2 (d) 4
  12. 12.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 207 (c) 216 (d) 217
  13. 13.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  14. 14.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 432 (c) 540 (d) 541
  15. 15.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) 24 (b) 63 (c) 7 (d) 21
  16. 16.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 15 (d) 5
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 15 (b) 4 (c) 14 (d) 13
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 19 (b) 18 (c) 7 (d) 17
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 14 (b) 13 (c) 3 (d) 15
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 85? (a) 8 (b) 20 (c) 18 (d) 19
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 37? (a) 1 (b) 4 (c) 3 (d) 2
  22. 22.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 426 (c) 436 (d) 362
  23. 23.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 43 (b) 34 (c) 44 (d) 52
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 19 (d) 18
  25. 25.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) 42 (c) 13 (d) 39
  26. 26.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 246 (c) 262 (d) 261
  27. 27.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  28. 28.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  29. 29.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) 18 (b) 15 (c) 45 (d) 5
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 19 (d) 18
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 8 (b) 4 (c) 5 (d) 7
  32. 32.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) 10 (b) 90 (c) 30 (d) 33
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 11 (b) 9 (c) 6 (d) 12
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 6 (b) 17 (c) 16 (d) 15
  35. 35.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 119 (c) 110 (d) 120
  36. 36.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) 8 (b) 27 (c) 24 (d) 72
  37. 37.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 125 (c) 134 (d) 126
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 65? (a) 5 (b) 7 (c) 4 (d) 6
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 68? (a) 16 (b) 17 (c) 6 (d) 18
  40. 40.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 553 (c) 543 (d) 440

Answer key

  1. 5
  2. 18
  3. 19
  4. 9
  5. 16
  6. 8
  7. 42
  8. 48
  9. 109
  10. 19
  11. 4
  12. 216
  13. 4
  14. 540
  15. 21
  16. 5
  17. 14
  18. 18
  19. 14
  20. 19
  21. 3
  22. 435
  23. 43
  24. 18
  25. 39
  26. 261
  27. 2
  28. 9
  29. 15
  30. 18
  31. 7
  32. 30
  33. 11
  34. 16
  35. 119
  36. 24
  37. 125
  38. 6
  39. 17
  40. 552

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