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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 233 · 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 6? (a) 7 (b) 10 (c) 5 (d) 6
  2. 2.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 134 (c) 126 (d) 125
  3. 3.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 63 (c) 54 (d) 64
  4. 4.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
  5. 5.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) 16 (c) 48 (d) 144
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 16 (b) 17 (c) 15 (d) 5
  7. 7.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) 27 (c) 30 (d) 9
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 18 (b) 8 (c) 19 (d) 17
  9. 9.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) 207 (b) 72 (c) 23 (d) 69
  10. 10.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) 42 (c) 14 (d) 45
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 11 (b) 14 (c) 13 (d) 9
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 15 (b) 17 (c) 16 (d) 6
  13. 13.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) 153 (b) 54 (c) 17 (d) 51
  14. 14.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 296 (b) 337 (c) 336 (d) 327
  15. 15.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) 24 (d) 72
  16. 16.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) 33 (b) 36 (c) 11 (d) 99
  17. 17.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
  18. 18.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 380 (c) 463 (d) 453
  19. 19.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) 24 (b) 8 (c) 27 (d) 72
  20. 20.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 1 (b) 2 (c) 4 (d) 3
  22. 22.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 1 (b) 4 (c) 3 (d) 2
  24. 24.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  25. 25.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
  26. 26.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 399 (c) 338 (d) 390
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 7 (b) 5 (c) 4 (d) 6
  28. 28.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) 21 (b) 63 (c) 24 (d) 7
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 67? (a) 7 (b) 6 (c) 5 (d) 8
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 5 (b) 4 (c) 3 (d) 6
  31. 31.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 213 (c) 214 (d) 204
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 17 (b) 18 (c) 7 (d) 19
  33. 33.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 480 (c) 613 (d) 603
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 14 (b) 4 (c) 15 (d) 16
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 19 (b) 20 (c) 9 (d) 21
  36. 36.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 18 (b) 16 (c) 7 (d) 17
  38. 38.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 630 (b) 640 (c) 639 (d) 498
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 14 (b) 3 (c) 15 (d) 13
  40. 40.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 302 (c) 336 (d) 345

Answer key

  1. 6
  2. 125
  3. 63
  4. 8
  5. 48
  6. 16
  7. 27
  8. 18
  9. 69
  10. 42
  11. 13
  12. 16
  13. 51
  14. 336
  15. 72
  16. 33
  17. 7
  18. 462
  19. 24
  20. 8
  21. 3
  22. 5
  23. 3
  24. 4
  25. 9
  26. 399
  27. 6
  28. 21
  29. 7
  30. 5
  31. 213
  32. 18
  33. 612
  34. 15
  35. 20
  36. 9
  37. 17
  38. 639
  39. 14
  40. 345

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