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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 995 · 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 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) 48 (b) 51 (c) 16 (d) 144
  2. 2.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 8 (d) 7
  3. 3.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  4. 4.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
  5. 5.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 30? (a) 2 (b) 4 (c) 3 (d) 1
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 16 (b) 17 (c) 5 (d) 15
  8. 8.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 22 (c) 31 (d) 40
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 79? (a) 9 (b) 8 (c) 6 (d) 7
  10. 10.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 412 (c) 511 (d) 501
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 71? (a) 16 (b) 7 (c) 17 (d) 18
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 15 (b) 14 (c) 13 (d) 3
  13. 13.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 93 (b) 84 (c) 102 (d) 94
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 16 (b) 18 (c) 17 (d) 6
  15. 15.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 291 (c) 301 (d) 272
  16. 16.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
  17. 17.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 143 (b) 152 (c) 144 (d) 134
  18. 18.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) 117 (b) 13 (c) 42 (d) 39
  19. 19.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 85 (b) 76 (c) 94 (d) 86
  20. 20.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 37 (b) 38 (c) 28 (d) 46
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 13 (b) 14 (c) 12 (d) 3
  22. 22.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) 19 (b) 60 (c) 171 (d) 57
  23. 23.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 42 (c) 51 (d) 52
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 19 (d) 18
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 7 (b) 3 (c) 4 (d) 6
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 2 (b) 3 (c) 5 (d) 4
  27. 27.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) 18 (b) 21 (c) 6 (d) 54
  28. 28.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) 66 (b) 189 (c) 21 (d) 63
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 4 (b) 3 (c) 5 (d) 2
  30. 30.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 170 (c) 179 (d) 188
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 14 (b) 12 (c) 3 (d) 13
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 14 (b) 15 (c) 16 (d) 4
  33. 33.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 183 (b) 192 (c) 193 (d) 200
  34. 34.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
  35. 35.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 116 (c) 108 (d) 107
  36. 36.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) 12 (b) 39 (c) 108 (d) 36
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 72? (a) 6 (b) 5 (c) 8 (d) 7
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 85? (a) 9 (b) 6 (c) 8 (d) 7
  39. 39.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 432 (c) 441 (d) 442
  40. 40.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) 27 (b) 24 (c) 72 (d) 8

Answer key

  1. 48
  2. 7
  3. 3
  4. 2
  5. 8
  6. 3
  7. 16
  8. 31
  9. 8
  10. 510
  11. 17
  12. 14
  13. 93
  14. 17
  15. 300
  16. 9
  17. 143
  18. 39
  19. 85
  20. 37
  21. 13
  22. 57
  23. 51
  24. 19
  25. 6
  26. 4
  27. 18
  28. 63
  29. 4
  30. 179
  31. 13
  32. 15
  33. 192
  34. 4
  35. 107
  36. 36
  37. 7
  38. 8
  39. 441
  40. 24

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