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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 742 · 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 16? (a) 3 (b) 2 (c) 17 (d) 4
  2. 2.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) 144 (b) 16 (c) 51 (d) 48
  3. 3.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 433 (c) 432 (d) 423
  4. 4.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) 6 (b) 54 (c) 18 (d) 21
  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) 8 (b) 27 (c) 24 (d) 72
  6. 6.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 15 (b) 16 (c) 14 (d) 4
  8. 8.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 10 (d) 11
  9. 9.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) 216 (b) 72 (c) 75 (d) 24
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 76? (a) 8 (b) 6 (c) 5 (d) 7
  11. 11.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  12. 12.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) 54 (b) 162 (c) 18 (d) 57
  13. 13.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  14. 14.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) 63 (c) 24 (d) 21
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 68? (a) 6 (b) 18 (c) 17 (d) 16
  16. 16.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 153 (b) 144 (c) 154 (d) 162
  17. 17.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) 42 (b) 117 (c) 13 (d) 39
  18. 18.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  19. 19.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) 99 (b) 11 (c) 36 (d) 33
  20. 20.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) 27 (c) 81 (d) 9
  21. 21.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 508 (c) 507 (d) 410
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 14 (d) 15
  23. 23.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 5 (b) 6 (c) 7 (d) 4
  25. 25.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 462 (c) 586 (d) 576
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 19 (b) 9 (c) 20 (d) 21
  27. 27.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 471 (b) 462 (c) 472 (d) 386
  28. 28.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
  29. 29.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 261 (c) 246 (d) 262
  30. 30.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 338 (b) 400 (c) 390 (d) 399
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 17 (b) 7 (c) 18 (d) 19
  32. 32.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 304 (c) 303 (d) 274
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 18 (b) 19 (c) 7 (d) 17
  34. 34.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) 60 (b) 57 (c) 19 (d) 171
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 73? (a) 18 (b) 17 (c) 7 (d) 16
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 15 (b) 14 (c) 13 (d) 3
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 4 (b) 3 (c) 2 (d) 5
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 14 (b) 4 (c) 16 (d) 15
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 94? (a) 9 (b) 19 (c) 20 (d) 21
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 6 (b) 5 (c) 4 (d) 3

Answer key

  1. 3
  2. 48
  3. 432
  4. 18
  5. 24
  6. 7
  7. 15
  8. 9
  9. 72
  10. 7
  11. 9
  12. 54
  13. 8
  14. 21
  15. 17
  16. 153
  17. 39
  18. 3
  19. 33
  20. 27
  21. 507
  22. 15
  23. 6
  24. 6
  25. 585
  26. 20
  27. 471
  28. 8
  29. 261
  30. 399
  31. 18
  32. 303
  33. 18
  34. 57
  35. 17
  36. 14
  37. 4
  38. 15
  39. 20
  40. 5

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