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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 48 · 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 two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  2. 2.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) 13 (b) 39 (c) 117 (d) 42
  3. 3.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 3 (b) 2 (c) 5 (d) 4
  5. 5.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
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 45? (a) 5 (b) 4 (c) 2 (d) 3
  7. 7.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 185 (b) 186 (c) 176 (d) 194
  8. 8.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 375 (c) 366 (d) 322
  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) 12 (b) 36 (c) 108 (d) 39
  10. 10.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) 66 (b) 69 (c) 198 (d) 22
  11. 11.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) 7 (c) 63 (d) 21
  12. 12.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 289 (b) 279 (c) 264 (d) 288
  13. 13.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 88? (a) 8 (b) 19 (c) 18 (d) 20
  15. 15.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 583 (b) 582 (c) 460 (d) 573
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 16 (b) 18 (c) 6 (d) 17
  17. 17.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 17 (b) 6 (c) 15 (d) 16
  19. 19.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
  20. 20.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) 135 (b) 45 (c) 15 (d) 48
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 19 (b) 18 (c) 9 (d) 20
  22. 22.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) 54 (b) 51 (c) 153 (d) 17
  23. 23.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 56 (c) 46 (d) 55
  24. 24.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) 23 (b) 72 (c) 69 (d) 207
  25. 25.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  26. 26.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) 144 (c) 51 (d) 48
  27. 27.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) 20 (b) 60 (c) 180 (d) 63
  28. 28.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 183 (b) 174 (c) 192 (d) 184
  29. 29.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
  30. 30.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
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 68? (a) 8 (b) 5 (c) 7 (d) 6
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 17 (b) 18 (c) 6 (d) 16
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 9 (b) 20 (c) 19 (d) 21
  34. 34.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 18 (b) 6 (c) 17 (d) 16
  36. 36.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 426 (c) 531 (d) 532
  37. 37.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) 11 (b) 33 (c) 36 (d) 99
  38. 38.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) 171 (c) 60 (d) 57
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 73? (a) 7 (b) 16 (c) 17 (d) 18
  40. 40.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 12 (d) 9

Answer key

  1. 2
  2. 39
  3. 6
  4. 4
  5. 24
  6. 4
  7. 185
  8. 375
  9. 36
  10. 66
  11. 21
  12. 288
  13. 6
  14. 19
  15. 582
  16. 17
  17. 3
  18. 16
  19. 27
  20. 45
  21. 19
  22. 51
  23. 55
  24. 69
  25. 5
  26. 48
  27. 60
  28. 183
  29. 42
  30. 18
  31. 7
  32. 17
  33. 20
  34. 3
  35. 17
  36. 531
  37. 33
  38. 57
  39. 17
  40. 8

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