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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 964 · 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 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
  2. 2.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 267 (b) 250 (c) 258 (d) 268
  3. 3.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) 54 (b) 162 (c) 18 (d) 57
  4. 4.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
  5. 5.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  6. 6.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 2 (b) 4 (c) 5 (d) 3
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 8 (b) 19 (c) 17 (d) 18
  9. 9.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
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 18 (b) 17 (c) 8 (d) 19
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 93? (a) 19 (b) 20 (c) 9 (d) 18
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11
  13. 13.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 5 (b) 6 (c) 7 (d) 4
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 2 (b) 3 (c) 1 (d) 4
  16. 16.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) 42 (c) 13 (d) 117
  17. 17.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) 10 (b) 30 (c) 33 (d) 90
  18. 18.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) 24 (b) 21 (c) 7 (d) 63
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 19 (b) 20 (c) 9 (d) 21
  20. 20.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 149 (c) 150 (d) 140
  21. 21.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  22. 22.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  23. 23.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 607 (c) 606 (d) 476
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 3 (b) 4 (c) 6 (d) 5
  25. 25.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 402 (c) 346 (d) 411
  26. 26.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 16 (b) 18 (c) 17 (d) 7
  28. 28.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  29. 29.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 380 (b) 463 (c) 453 (d) 462
  30. 30.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 18 (b) 16 (c) 17 (d) 6
  32. 32.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 61 (c) 70 (d) 62
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 18 (b) 19 (c) 9 (d) 16
  34. 34.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) 9 (c) 30 (d) 27
  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.How many times is the digit 5 written when you write all the numbers from 1 to 78? (a) 19 (b) 17 (c) 7 (d) 18
  37. 37.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
  38. 38.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 17 (b) 6 (c) 15 (d) 16
  40. 40.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) 135 (d) 48

Answer key

  1. 66
  2. 267
  3. 54
  4. 63
  5. 7
  6. 6
  7. 4
  8. 18
  9. 42
  10. 18
  11. 19
  12. 9
  13. 3
  14. 6
  15. 3
  16. 39
  17. 30
  18. 21
  19. 20
  20. 149
  21. 2
  22. 7
  23. 606
  24. 5
  25. 411
  26. 2
  27. 17
  28. 6
  29. 462
  30. 4
  31. 17
  32. 61
  33. 18
  34. 27
  35. 48
  36. 18
  37. 24
  38. 4
  39. 16
  40. 45

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