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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 704 · 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 times is the digit 3 written when you write all the numbers from 1 to 63? (a) 16 (b) 6 (c) 17 (d) 18
  2. 2.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) 171 (d) 19
  3. 3.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  4. 4.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
  5. 5.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 74? (a) 18 (b) 16 (c) 17 (d) 7
  7. 7.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  8. 8.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 24 (b) 34 (c) 42 (d) 33
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 71? (a) 18 (b) 16 (c) 17 (d) 7
  10. 10.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 330 (c) 298 (d) 340
  11. 11.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) 342 (c) 351 (d) 352
  12. 12.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) 48 (c) 144 (d) 16
  13. 13.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) 57 (b) 54 (c) 162 (d) 18
  14. 14.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) 46 (c) 55 (d) 64
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 62? (a) 6 (b) 5 (c) 7 (d) 4
  16. 16.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) 39 (c) 13 (d) 117
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 10 (b) 9 (c) 8 (d) 11
  18. 18.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) 11 (b) 33 (c) 99 (d) 36
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 19 (b) 9 (c) 21 (d) 20
  20. 20.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) 66 (d) 22
  21. 21.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 144 (c) 136 (d) 135
  22. 22.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) 27 (b) 81 (c) 30 (d) 9
  23. 23.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 6 (d) 15
  24. 24.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) 18 (b) 54 (c) 6 (d) 21
  25. 25.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  26. 26.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 603 (c) 613 (d) 612
  27. 27.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 552 (c) 440 (d) 553
  28. 28.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 400 (c) 492 (d) 493
  29. 29.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 50 (c) 59 (d) 60
  30. 30.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 19 (b) 20 (c) 9 (d) 21
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 18 (b) 20 (c) 19 (d) 8
  33. 33.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 241 (b) 231 (c) 232 (d) 240
  34. 34.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 12 (c) 39 (d) 36
  35. 35.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 3 (b) 7 (c) 6 (d) 4
  37. 37.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 40 (c) 50 (d) 49
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 19 (b) 7 (c) 17 (d) 18
  39. 39.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 8 (d) 10
  40. 40.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4

Answer key

  1. 17
  2. 57
  3. 4
  4. 4
  5. 7
  6. 17
  7. 2
  8. 33
  9. 17
  10. 339
  11. 351
  12. 48
  13. 54
  14. 55
  15. 6
  16. 39
  17. 10
  18. 33
  19. 20
  20. 66
  21. 135
  22. 27
  23. 5
  24. 18
  25. 8
  26. 612
  27. 552
  28. 492
  29. 59
  30. 2
  31. 20
  32. 19
  33. 240
  34. 36
  35. 3
  36. 6
  37. 49
  38. 18
  39. 9
  40. 3

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