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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 649 · 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.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
  2. 2.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 10 (d) 9
  3. 3.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3
  4. 4.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) 21 (b) 66 (c) 63 (d) 189
  5. 5.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 400 (c) 399 (d) 338
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 19 (b) 18 (c) 20 (d) 8
  7. 7.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) 72 (b) 216 (c) 75 (d) 24
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 9 (b) 18 (c) 20 (d) 19
  9. 9.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 71? (a) 7 (b) 17 (c) 16 (d) 18
  11. 11.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) 14 (b) 126 (c) 45 (d) 42
  12. 12.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 5 (d) 14
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 12 (b) 14 (c) 13 (d) 3
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 16 (b) 6 (c) 17 (d) 18
  15. 15.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 282 (c) 291 (d) 266
  16. 16.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  17. 17.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 30 (b) 48 (c) 40 (d) 39
  18. 18.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 484 (c) 394 (d) 483
  19. 19.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 106 (c) 115 (d) 116
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 8 (b) 7 (c) 5 (d) 6
  21. 21.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 15 (c) 45 (d) 48
  22. 22.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) 54 (b) 18 (c) 21 (d) 6
  23. 23.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 71 (c) 62 (d) 72
  24. 24.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 8 (d) 6
  25. 25.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 460 (c) 583 (d) 573
  26. 26.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  27. 27.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 429 (c) 420 (d) 358
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 37? (a) 4 (b) 1 (c) 2 (d) 3
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 17 (b) 16 (c) 15 (d) 5
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 3 (b) 2 (c) 1 (d) 4
  31. 31.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 639 (b) 630 (c) 640 (d) 498
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 3 (b) 5 (c) 4 (d) 2
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 19 (b) 9 (c) 18 (d) 20
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 4 (b) 3 (c) 5 (d) 2
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 3 (b) 15 (c) 13 (d) 14
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 6 (b) 3 (c) 5 (d) 4
  37. 37.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 343 (b) 300 (c) 333 (d) 342
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 6 (b) 17 (c) 18 (d) 16
  39. 39.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
  40. 40.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6

Answer key

  1. 21
  2. 8
  3. 2
  4. 63
  5. 399
  6. 19
  7. 72
  8. 19
  9. 9
  10. 17
  11. 42
  12. 6
  13. 13
  14. 17
  15. 291
  16. 3
  17. 39
  18. 483
  19. 115
  20. 7
  21. 45
  22. 18
  23. 71
  24. 7
  25. 582
  26. 2
  27. 429
  28. 3
  29. 16
  30. 3
  31. 639
  32. 4
  33. 19
  34. 4
  35. 14
  36. 5
  37. 342
  38. 17
  39. 7
  40. 6

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