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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 197 · 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 14? (a) 6 (b) 4 (c) 15 (d) 5
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 55? (a) 16 (b) 15 (c) 5 (d) 17
  3. 3.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) 63 (b) 189 (c) 66 (d) 21
  4. 4.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) 171 (b) 60 (c) 19 (d) 57
  5. 5.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  6. 6.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  7. 7.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) 144 (c) 48 (d) 16
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 43? (a) 3 (b) 5 (c) 4 (d) 2
  9. 9.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 247 (c) 237 (d) 236
  10. 10.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 231 (c) 232 (d) 222
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 17 (b) 5 (c) 15 (d) 16
  12. 12.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  13. 13.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  14. 14.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) 36 (b) 11 (c) 99 (d) 33
  15. 15.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 306 (c) 307 (d) 297
  16. 16.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  17. 17.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 137 (c) 128 (d) 138
  18. 18.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 505 (b) 408 (c) 495 (d) 504
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 88? (a) 8 (b) 17 (c) 19 (d) 18
  20. 20.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  21. 21.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 24 (b) 42 (c) 34 (d) 33
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 12 (b) 14 (c) 3 (d) 13
  23. 23.The numbers 1 to 9 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) 18 (c) 15 (d) 5
  24. 24.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) 117 (d) 13
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 3 (b) 6 (c) 5 (d) 4
  26. 26.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) 54 (d) 6
  27. 27.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 136 (c) 118 (d) 127
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 17 (b) 16 (c) 18 (d) 7
  29. 29.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 16 (b) 18 (c) 6 (d) 17
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 20 (b) 19 (c) 21 (d) 9
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 68? (a) 15 (b) 6 (c) 17 (d) 16
  33. 33.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 336 (c) 346 (d) 302
  34. 34.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  35. 35.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) 90 (b) 33 (c) 10 (d) 30
  36. 36.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  37. 37.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 11 (d) 8
  38. 38.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
  39. 39.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) 198 (b) 69 (c) 22 (d) 66
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 16 (b) 17 (c) 6 (d) 18

Answer key

  1. 5
  2. 16
  3. 63
  4. 57
  5. 2
  6. 3
  7. 48
  8. 4
  9. 246
  10. 231
  11. 16
  12. 4
  13. 6
  14. 33
  15. 306
  16. 6
  17. 137
  18. 504
  19. 18
  20. 3
  21. 33
  22. 13
  23. 15
  24. 39
  25. 5
  26. 18
  27. 127
  28. 17
  29. 2
  30. 17
  31. 20
  32. 16
  33. 345
  34. 8
  35. 30
  36. 5
  37. 9
  38. 36
  39. 66
  40. 17

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