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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 535 · 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 2 written when you write all the numbers from 1 to 61? (a) 15 (b) 17 (c) 6 (d) 16
  2. 2.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) 54 (c) 51 (d) 17
  3. 3.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) 207 (b) 23 (c) 72 (d) 69
  4. 4.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 19 (b) 9 (c) 21 (d) 20
  6. 6.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  7. 7.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 616 (b) 615 (c) 606 (d) 482
  8. 8.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  9. 9.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) 39 (c) 36 (d) 12
  10. 10.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
  11. 11.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) 33 (b) 11 (c) 36 (d) 99
  12. 12.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 612 (c) 486 (d) 622
  13. 13.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 378 (c) 459 (d) 450
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 3 (b) 2 (c) 4 (d) 5
  15. 15.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) 69 (b) 198 (c) 22 (d) 66
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 31? (a) 1 (b) 3 (c) 2 (d) 4
  17. 17.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) 7 (b) 24 (c) 63 (d) 21
  18. 18.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 13 (b) 4 (c) 14 (d) 15
  20. 20.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
  21. 21.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) 72 (b) 24 (c) 27 (d) 8
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 18 (b) 19 (c) 7 (d) 17
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 88? (a) 8 (b) 20 (c) 19 (d) 18
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 1 (b) 4 (c) 3 (d) 2
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 18 (b) 20 (c) 8 (d) 19
  26. 26.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) 352 (c) 420 (d) 421
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 70? (a) 9 (b) 7 (c) 6 (d) 8
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 14 (b) 16 (c) 5 (d) 15
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 40? (a) 5 (b) 4 (c) 2 (d) 3
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 18 (b) 20 (c) 8 (d) 19
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 3 (b) 9 (c) 8 (d) 10
  32. 32.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) 144 (b) 48 (c) 51 (d) 16
  33. 33.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 576 (c) 585 (d) 586
  34. 34.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 14 (b) 13 (c) 15 (d) 3
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 17 (b) 16 (c) 15 (d) 5
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 83? (a) 19 (b) 18 (c) 8 (d) 20
  38. 38.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 390 (c) 478 (d) 477
  39. 39.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 69? (a) 6 (b) 18 (c) 17 (d) 16

Answer key

  1. 16
  2. 51
  3. 69
  4. 2
  5. 20
  6. 4
  7. 615
  8. 8
  9. 36
  10. 7
  11. 33
  12. 621
  13. 459
  14. 4
  15. 66
  16. 3
  17. 21
  18. 8
  19. 14
  20. 57
  21. 24
  22. 18
  23. 19
  24. 3
  25. 19
  26. 420
  27. 8
  28. 15
  29. 4
  30. 19
  31. 9
  32. 48
  33. 585
  34. 2
  35. 14
  36. 16
  37. 19
  38. 477
  39. 5
  40. 17

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