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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 597 · 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 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 313 (c) 280 (d) 303
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 96? (a) 16 (b) 17 (c) 14 (d) 9
  3. 3.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 4 (b) 5 (c) 6 (d) 7
  5. 5.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
  6. 6.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 103 (b) 94 (c) 104 (d) 112
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 6 (b) 18 (c) 17 (d) 16
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 5 (b) 8 (c) 6 (d) 7
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 88? (a) 19 (b) 18 (c) 20 (d) 8
  10. 10.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 5 (d) 3
  11. 11.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 606 (c) 476 (d) 607
  12. 12.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 549 (c) 444 (d) 559
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 2 (b) 5 (c) 4 (d) 3
  14. 14.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 102 (c) 101 (d) 110
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 52? (a) 5 (b) 3 (c) 4 (d) 6
  16. 16.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 253 (b) 252 (c) 240 (d) 243
  17. 17.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) 42 (c) 45 (d) 126
  18. 18.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 124 (c) 115 (d) 116
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 4 (b) 15 (c) 14 (d) 16
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 4 (b) 5 (c) 2 (d) 3
  21. 21.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 226 (c) 216 (d) 225
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 15 (b) 3 (c) 14 (d) 13
  23. 23.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) 21 (b) 6 (c) 18 (d) 54
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 67? (a) 8 (b) 5 (c) 7 (d) 6
  25. 25.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) 27 (c) 24 (d) 8
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 99? (a) 21 (b) 9 (c) 19 (d) 20
  27. 27.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 81 (c) 9 (d) 30
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 15 (b) 5 (c) 16 (d) 17
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 97? (a) 20 (b) 19 (c) 9 (d) 18
  30. 30.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) 189 (c) 21 (d) 63
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 20 (b) 18 (c) 19 (d) 9
  32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 8 (b) 7 (c) 5 (d) 6
  33. 33.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) 15 (c) 48 (d) 135
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 18 (b) 16 (c) 7 (d) 17
  35. 35.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
  36. 36.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 11 (b) 33 (c) 36 (d) 99
  37. 37.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 88 (c) 79 (d) 70
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 18 (b) 19 (c) 7 (d) 17
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 4 (b) 16 (c) 15 (d) 14
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 17 (b) 18 (c) 16 (d) 6

Answer key

  1. 312
  2. 16
  3. 7
  4. 6
  5. 3
  6. 103
  7. 17
  8. 7
  9. 19
  10. 4
  11. 606
  12. 558
  13. 4
  14. 101
  15. 5
  16. 252
  17. 42
  18. 115
  19. 15
  20. 4
  21. 225
  22. 14
  23. 18
  24. 7
  25. 24
  26. 20
  27. 27
  28. 16
  29. 19
  30. 63
  31. 19
  32. 7
  33. 45
  34. 17
  35. 7
  36. 33
  37. 79
  38. 18
  39. 15
  40. 17

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