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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 198 · 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 6 written when you write all the numbers from 1 to 49? (a) 5 (b) 6 (c) 3 (d) 4
  2. 2.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) 63 (d) 21
  3. 3.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) 27 (b) 24 (c) 8 (d) 72
  4. 4.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) 57 (b) 171 (c) 19 (d) 60
  5. 5.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 102 (c) 93 (d) 84
  6. 6.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) 57 (c) 54 (d) 162
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 1 (b) 4 (c) 3 (d) 2
  8. 8.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
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 5 (b) 2 (c) 3 (d) 4
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 5 (b) 16 (c) 17 (d) 15
  11. 11.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) 112 (c) 94 (d) 104
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 55? (a) 16 (b) 5 (c) 15 (d) 17
  13. 13.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 149 (b) 158 (c) 150 (d) 140
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 42? (a) 2 (b) 5 (c) 4 (d) 3
  15. 15.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) 216 (c) 75 (d) 24
  16. 16.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 492 (c) 400 (d) 493
  17. 17.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 193 (b) 200 (c) 183 (d) 192
  18. 18.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) 54 (c) 17 (d) 153
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 7 (b) 8 (c) 9 (d) 6
  20. 20.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 290 (c) 327 (d) 318
  21. 21.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  22. 22.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  23. 23.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 495 (c) 504 (d) 505
  24. 24.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 15 (b) 4 (c) 14 (d) 13
  26. 26.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) 21 (b) 7 (c) 63 (d) 24
  27. 27.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 178 (c) 168 (d) 177
  28. 28.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 8 (b) 19 (c) 18 (d) 17
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 6 (b) 7 (c) 9 (d) 8
  31. 31.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) 22 (b) 69 (c) 66 (d) 198
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 7 (b) 16 (c) 18 (d) 17
  33. 33.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) 126 (b) 14 (c) 45 (d) 42
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 4 (b) 5 (c) 6 (d) 3
  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 times is the digit 9 written when you write all the numbers from 1 to 48? (a) 5 (b) 4 (c) 3 (d) 2
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 7 (b) 17 (c) 16 (d) 18
  38. 38.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) 23 (b) 72 (c) 69 (d) 207
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 5 (b) 17 (c) 16 (d) 15
  40. 40.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) 90 (b) 30 (c) 10 (d) 33

Answer key

  1. 5
  2. 63
  3. 24
  4. 57
  5. 93
  6. 54
  7. 3
  8. 39
  9. 4
  10. 16
  11. 103
  12. 16
  13. 149
  14. 4
  15. 72
  16. 492
  17. 192
  18. 51
  19. 8
  20. 327
  21. 7
  22. 4
  23. 504
  24. 2
  25. 14
  26. 21
  27. 177
  28. 8
  29. 18
  30. 8
  31. 66
  32. 17
  33. 42
  34. 5
  35. 4
  36. 4
  37. 17
  38. 69
  39. 16
  40. 30

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