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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 849 · 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 9? (a) 8 (b) 11 (c) 9 (d) 10
  2. 2.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 10 (d) 7
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  4. 4.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 489 (c) 398 (d) 480
  5. 5.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) 216 (c) 72 (d) 24
  6. 6.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 15 (b) 16 (c) 5 (d) 14
  8. 8.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) 307 (d) 306
  9. 9.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
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 20 (b) 19 (c) 18 (d) 8
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 5 (b) 16 (c) 15 (d) 17
  12. 12.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 622 (b) 621 (c) 486 (d) 612
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 59? (a) 15 (b) 17 (c) 5 (d) 16
  14. 14.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 171 (c) 180 (d) 162
  15. 15.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) 162 (b) 18 (c) 57 (d) 54
  16. 16.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) 17 (b) 54 (c) 153 (d) 51
  17. 17.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 83 (c) 92 (d) 74
  18. 18.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 8 (d) 7
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 61? (a) 7 (b) 6 (c) 4 (d) 5
  20. 20.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 55 (c) 46 (d) 64
  21. 21.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 7 (d) 8
  22. 22.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 352 (c) 342 (d) 351
  23. 23.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 7 (d) 12
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 99? (a) 9 (b) 20 (c) 21 (d) 19
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 16 (b) 15 (c) 4 (d) 14
  26. 26.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 60? (a) 8 (b) 7 (c) 6 (d) 5
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 19 (b) 18 (c) 9 (d) 20
  29. 29.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 15 (b) 16 (c) 4 (d) 14
  31. 31.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) 7 (b) 24 (c) 21 (d) 63
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 58? (a) 6 (b) 4 (c) 3 (d) 5
  33. 33.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) 180 (b) 60 (c) 20 (d) 63
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 33? (a) 7 (b) 3 (c) 9 (d) 8
  35. 35.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) 9 (d) 27
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 19 (b) 17 (c) 7 (d) 18
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 9 (b) 8 (c) 6 (d) 7
  38. 38.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) 10 (c) 33 (d) 30
  39. 39.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 402 (c) 340 (d) 403
  40. 40.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7

Answer key

  1. 9
  2. 6
  3. 5
  4. 489
  5. 72
  6. 5
  7. 15
  8. 306
  9. 24
  10. 19
  11. 16
  12. 621
  13. 16
  14. 171
  15. 54
  16. 51
  17. 83
  18. 7
  19. 6
  20. 55
  21. 7
  22. 351
  23. 8
  24. 20
  25. 15
  26. 9
  27. 7
  28. 19
  29. 8
  30. 15
  31. 21
  32. 5
  33. 60
  34. 8
  35. 27
  36. 18
  37. 8
  38. 30
  39. 402
  40. 6

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