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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 740 · 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 times is the digit 4 written when you write all the numbers from 1 to 50? (a) 5 (b) 14 (c) 15 (d) 16
  2. 2.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 9 (b) 20 (c) 18 (d) 19
  4. 4.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) 24 (b) 27 (c) 72 (d) 8
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 90? (a) 20 (b) 9 (c) 18 (d) 19
  6. 6.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 41 (c) 42 (d) 32
  7. 7.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 153 (c) 54 (d) 51
  8. 8.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) 69 (c) 22 (d) 66
  9. 9.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 140 (c) 139 (d) 148
  10. 10.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 170 (c) 180 (d) 179
  11. 11.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 255 (c) 256 (d) 242
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 18 (b) 16 (c) 7 (d) 17
  13. 13.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 158 (c) 148 (d) 157
  14. 14.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) 63 (b) 66 (c) 21 (d) 189
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 3 (b) 4 (c) 6 (d) 5
  16. 16.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
  17. 17.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
  18. 18.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 488 (c) 615 (d) 625
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 80? (a) 8 (b) 19 (c) 18 (d) 17
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 18 (b) 6 (c) 17 (d) 16
  21. 21.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 198 (c) 190 (d) 189
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 16 (b) 14 (c) 15 (d) 4
  23. 23.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 8 (d) 10
  24. 24.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) 18 (c) 5 (d) 45
  25. 25.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 15 (d) 4
  26. 26.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 451 (b) 372 (c) 441 (d) 450
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 19 (b) 18 (c) 8 (d) 17
  28. 28.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) 77 (c) 78 (d) 68
  29. 29.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) 18 (b) 6 (c) 21 (d) 54
  30. 30.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) 135 (b) 48 (c) 45 (d) 15
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 4 (b) 15 (c) 16 (d) 14
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 15 (b) 16 (c) 14 (d) 4
  33. 33.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) 110 (c) 109 (d) 100
  34. 34.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 168 (c) 167 (d) 158
  35. 35.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  36. 36.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 8 (b) 5 (c) 7 (d) 6
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 17 (b) 19 (c) 7 (d) 18
  39. 39.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 30? (a) 3 (b) 1 (c) 2 (d) 4

Answer key

  1. 15
  2. 2
  3. 19
  4. 24
  5. 19
  6. 41
  7. 51
  8. 66
  9. 139
  10. 179
  11. 255
  12. 17
  13. 157
  14. 63
  15. 5
  16. 39
  17. 3
  18. 624
  19. 18
  20. 17
  21. 189
  22. 15
  23. 9
  24. 15
  25. 5
  26. 450
  27. 18
  28. 77
  29. 18
  30. 45
  31. 15
  32. 15
  33. 109
  34. 167
  35. 4
  36. 4
  37. 7
  38. 18
  39. 8
  40. 3

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