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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 445 · 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.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) 39 (b) 12 (c) 108 (d) 36
  2. 2.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 138 (c) 137 (d) 146
  3. 3.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) 75 (b) 72 (c) 24 (d) 216
  4. 4.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) 99 (b) 33 (c) 11 (d) 36
  5. 5.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
  6. 6.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) 69 (d) 66
  7. 7.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
  8. 8.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  9. 9.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) 207 (c) 72 (d) 69
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 92? (a) 20 (b) 18 (c) 19 (d) 9
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 5 (b) 2 (c) 4 (d) 3
  12. 12.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 618 (c) 484 (d) 619
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 4 (b) 13 (c) 15 (d) 14
  14. 14.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 157 (b) 148 (c) 158 (d) 166
  15. 15.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
  16. 16.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) 48 (b) 45 (c) 135 (d) 15
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 7 (b) 8 (c) 6 (d) 5
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 19 (b) 18 (c) 17 (d) 7
  19. 19.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) 189 (b) 63 (c) 21 (d) 66
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 3 (b) 2 (c) 4 (d) 5
  21. 21.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 310 (c) 348 (d) 358
  22. 22.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
  23. 23.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 409 (c) 399 (d) 344
  24. 24.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 345 (c) 302 (d) 346
  25. 25.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) 153 (b) 51 (c) 17 (d) 54
  26. 26.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 457 (c) 456 (d) 376
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 18 (b) 6 (c) 16 (d) 17
  28. 28.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 213 (b) 223 (c) 222 (d) 220
  29. 29.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  30. 30.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 5 (b) 7 (c) 6 (d) 4
  32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 98? (a) 19 (b) 20 (c) 21 (d) 9
  33. 33.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) 33 (b) 30 (c) 90 (d) 10
  34. 34.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 338 (b) 390 (c) 399 (d) 400
  35. 35.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) 51 (b) 48 (c) 144 (d) 16
  36. 36.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) 162 (b) 18 (c) 57 (d) 54
  37. 37.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 127 (b) 118 (c) 136 (d) 128
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 19 (b) 17 (c) 18 (d) 7
  39. 39.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) 45 (b) 5 (c) 15 (d) 18
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 19 (b) 9 (c) 20 (d) 21

Answer key

  1. 36
  2. 137
  3. 72
  4. 33
  5. 4
  6. 66
  7. 9
  8. 7
  9. 69
  10. 19
  11. 4
  12. 618
  13. 14
  14. 157
  15. 8
  16. 45
  17. 7
  18. 18
  19. 63
  20. 4
  21. 357
  22. 5
  23. 408
  24. 345
  25. 51
  26. 456
  27. 17
  28. 222
  29. 2
  30. 2
  31. 6
  32. 20
  33. 30
  34. 399
  35. 48
  36. 54
  37. 127
  38. 18
  39. 15
  40. 20

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