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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 406 · 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 4? (a) 10 (b) 5 (c) 4 (d) 3
  2. 2.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) 69 (b) 198 (c) 22 (d) 66
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  4. 4.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  5. 5.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
  6. 6.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  7. 7.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) 8 (c) 24 (d) 72
  8. 8.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  9. 9.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) 33 (b) 10 (c) 90 (d) 30
  10. 10.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) 18 (b) 162 (c) 54 (d) 57
  11. 11.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) 297 (c) 306 (d) 307
  12. 12.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
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 1 (b) 3 (c) 2 (d) 4
  14. 14.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 186 (c) 202 (d) 196
  15. 15.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 180 (c) 189 (d) 190
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 8 (b) 20 (c) 19 (d) 18
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 64? (a) 15 (b) 6 (c) 16 (d) 17
  18. 18.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) 75 (b) 24 (c) 72 (d) 216
  19. 19.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  20. 20.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 6 (d) 7
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 18 (b) 19 (c) 20 (d) 8
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 4 (b) 5 (c) 6 (d) 3
  23. 23.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 270 (c) 298 (d) 288
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 87? (a) 16 (b) 8 (c) 14 (d) 17
  25. 25.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) 16 (c) 144 (d) 51
  26. 26.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
  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) 21 (b) 6 (c) 18 (d) 54
  28. 28.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 216 (b) 225 (c) 226 (d) 222
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 15 (b) 14 (c) 16 (d) 4
  30. 30.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 204 (c) 189 (d) 199
  31. 31.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 456 (c) 376 (d) 457
  32. 32.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 81 (c) 90 (d) 72
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 9 (b) 19 (c) 18 (d) 20
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 96? (a) 19 (b) 20 (c) 9 (d) 21
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 8 (b) 6 (c) 5 (d) 7
  36. 36.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 2 (b) 4 (c) 3 (d) 5
  38. 38.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 568 (b) 567 (c) 450 (d) 558
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 58? (a) 5 (b) 4 (c) 6 (d) 7
  40. 40.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11

Answer key

  1. 4
  2. 66
  3. 5
  4. 2
  5. 2
  6. 8
  7. 24
  8. 3
  9. 30
  10. 54
  11. 306
  12. 57
  13. 3
  14. 195
  15. 189
  16. 19
  17. 16
  18. 72
  19. 5
  20. 7
  21. 19
  22. 5
  23. 297
  24. 16
  25. 48
  26. 15
  27. 18
  28. 225
  29. 15
  30. 198
  31. 456
  32. 81
  33. 19
  34. 20
  35. 7
  36. 7
  37. 4
  38. 567
  39. 6
  40. 9

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