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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 188 · 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 3 written when you write all the numbers from 1 to 40? (a) 4 (b) 14 (c) 15 (d) 13
  2. 2.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 4 (b) 16 (c) 15 (d) 14
  4. 4.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) 81 (b) 30 (c) 9 (d) 27
  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) 117 (b) 118 (c) 108 (d) 126
  6. 6.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) 171 (b) 60 (c) 19 (d) 57
  7. 7.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 420 (c) 352 (d) 421
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 18 (b) 20 (c) 8 (d) 19
  9. 9.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 490 (c) 398 (d) 489
  10. 10.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
  11. 11.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 213 (c) 214 (d) 204
  12. 12.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 31? (a) 4 (b) 2 (c) 3 (d) 1
  14. 14.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) 39 (b) 117 (c) 42 (d) 13
  15. 15.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 44 (c) 62 (d) 53
  16. 16.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) 189 (c) 66 (d) 21
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 33? (a) 7 (b) 8 (c) 3 (d) 9
  18. 18.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
  19. 19.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) 51 (b) 17 (c) 54 (d) 153
  20. 20.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 58 (c) 57 (d) 66
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 3 (b) 5 (c) 2 (d) 4
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 19 (b) 9 (c) 20 (d) 18
  23. 23.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 58? (a) 17 (b) 5 (c) 15 (d) 16
  25. 25.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 5 (d) 14
  26. 26.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) 18 (b) 54 (c) 57 (d) 162
  27. 27.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
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 4 (b) 6 (c) 5 (d) 7
  29. 29.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) 72 (c) 27 (d) 24
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 14 (b) 15 (c) 16 (d) 4
  31. 31.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 12 (c) 39 (d) 36
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 18 (b) 19 (c) 17 (d) 7
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 58? (a) 17 (b) 5 (c) 16 (d) 15
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 4 (b) 14 (c) 15 (d) 16
  35. 35.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 219 (c) 220 (d) 218
  36. 36.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 10 (d) 6
  37. 37.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) 22 (c) 66 (d) 69
  38. 38.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
  39. 39.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 249 (c) 258 (d) 259
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 9 (b) 21 (c) 19 (d) 20

Answer key

  1. 14
  2. 5
  3. 15
  4. 27
  5. 117
  6. 57
  7. 420
  8. 19
  9. 489
  10. 261
  11. 213
  12. 2
  13. 3
  14. 39
  15. 53
  16. 63
  17. 8
  18. 4
  19. 51
  20. 57
  21. 4
  22. 19
  23. 5
  24. 16
  25. 6
  26. 54
  27. 18
  28. 6
  29. 24
  30. 15
  31. 36
  32. 18
  33. 16
  34. 15
  35. 219
  36. 7
  37. 66
  38. 8
  39. 258
  40. 20

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