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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 268 · 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 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) 27 (c) 24 (d) 72
  2. 2.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
  3. 3.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
  4. 4.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 2 (d) 1
  5. 5.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) 30 (b) 81 (c) 27 (d) 9
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 1 (b) 4 (c) 2 (d) 3
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 6 (b) 16 (c) 18 (d) 17
  8. 8.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 63? (a) 6 (b) 5 (c) 7 (d) 4
  10. 10.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 385 (b) 375 (c) 384 (d) 328
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 65? (a) 17 (b) 16 (c) 18 (d) 6
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 18 (d) 7
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 81? (a) 17 (b) 18 (c) 8 (d) 19
  14. 14.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 99 (b) 100 (c) 90 (d) 108
  15. 15.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 151 (c) 160 (d) 142
  16. 16.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 67 (c) 58 (d) 68
  17. 17.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  18. 18.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) 16 (b) 51 (c) 144 (d) 48
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 7 (b) 8 (c) 5 (d) 6
  20. 20.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 8 (d) 11
  21. 21.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  22. 22.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 286 (c) 276 (d) 285
  23. 23.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 73 (c) 64 (d) 74
  24. 24.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 5 (d) 16
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 50? (a) 6 (b) 5 (c) 4 (d) 3
  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) 24 (c) 63 (d) 7
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 10 (b) 11 (c) 3 (d) 12
  28. 28.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 475 (c) 465 (d) 388
  29. 29.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) 24 (c) 75 (d) 216
  30. 30.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 440 (b) 552 (c) 543 (d) 553
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 15 (b) 3 (c) 13 (d) 14
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 19 (b) 8 (c) 18 (d) 17
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 15 (b) 14 (c) 16 (d) 4
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 6 (b) 5 (c) 3 (d) 4
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 14 (b) 13 (c) 3 (d) 12
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 68? (a) 5 (b) 6 (c) 8 (d) 7
  37. 37.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) 33 (c) 30 (d) 90
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 96? (a) 9 (b) 14 (c) 17 (d) 16
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 7 (b) 17 (c) 18 (d) 19
  40. 40.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

Answer key

  1. 24
  2. 3
  3. 9
  4. 2
  5. 27
  6. 3
  7. 17
  8. 8
  9. 6
  10. 384
  11. 17
  12. 18
  13. 18
  14. 99
  15. 151
  16. 67
  17. 5
  18. 48
  19. 7
  20. 9
  21. 6
  22. 285
  23. 73
  24. 4
  25. 5
  26. 21
  27. 11
  28. 474
  29. 72
  30. 552
  31. 14
  32. 18
  33. 15
  34. 5
  35. 13
  36. 7
  37. 30
  38. 16
  39. 18
  40. 33

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