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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 2 · 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 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) 24 (c) 72 (d) 216
  2. 2.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 6 (d) 7
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 5 (b) 3 (c) 4 (d) 6
  4. 4.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 321 (c) 331 (d) 330
  5. 5.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) 6 (b) 21 (c) 54 (d) 18
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 14 (b) 15 (c) 4 (d) 13
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 18 (b) 17 (c) 7 (d) 16
  8. 8.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 589 (b) 464 (c) 579 (d) 588
  9. 9.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) 60 (b) 171 (c) 19 (d) 57
  10. 10.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 303 (c) 304 (d) 274
  11. 11.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
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 17 (b) 6 (c) 16 (d) 18
  13. 13.The numbers 16 to 24 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) 180 (c) 20 (d) 60
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 89? (a) 8 (b) 19 (c) 20 (d) 18
  15. 15.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
  16. 16.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 453 (b) 380 (c) 463 (d) 462
  17. 17.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 366 (c) 432 (d) 441
  18. 18.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) 45 (c) 42 (d) 14
  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) 21 (b) 66 (c) 189 (d) 63
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 16 (b) 17 (c) 15 (d) 5
  21. 21.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 3 (d) 1
  22. 22.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) 346 (c) 302 (d) 345
  23. 23.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  24. 24.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 5 (b) 8 (c) 7 (d) 4
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 14 (b) 4 (c) 15 (d) 13
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 6 (b) 15 (c) 17 (d) 16
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 16 (b) 15 (c) 8 (d) 13
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 19 (b) 9 (c) 18 (d) 20
  30. 30.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) 36 (c) 33 (d) 11
  31. 31.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 583 (c) 460 (d) 582
  32. 32.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 8 (b) 20 (c) 19 (d) 18
  34. 34.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 388 (c) 475 (d) 474
  35. 35.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 5 (b) 3 (c) 2 (d) 4
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 73? (a) 16 (b) 17 (c) 18 (d) 7
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 61? (a) 7 (b) 5 (c) 6 (d) 4
  39. 39.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 18 (b) 20 (c) 19 (d) 8

Answer key

  1. 72
  2. 7
  3. 5
  4. 330
  5. 18
  6. 14
  7. 17
  8. 588
  9. 57
  10. 303
  11. 27
  12. 17
  13. 60
  14. 19
  15. 45
  16. 462
  17. 441
  18. 42
  19. 63
  20. 16
  21. 2
  22. 345
  23. 5
  24. 6
  25. 7
  26. 14
  27. 16
  28. 15
  29. 19
  30. 33
  31. 582
  32. 7
  33. 19
  34. 474
  35. 8
  36. 4
  37. 17
  38. 6
  39. 3
  40. 19

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