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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 973 · 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 6 written when you write all the numbers from 1 to 41? (a) 5 (b) 3 (c) 2 (d) 4
  2. 2.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 10 (d) 5
  3. 3.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
  4. 4.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 6 (d) 14
  5. 5.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 54? (a) 17 (b) 15 (c) 5 (d) 16
  7. 7.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
  8. 8.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) 15 (b) 135 (c) 48 (d) 45
  9. 9.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 624 (c) 625 (d) 488
  10. 10.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 481 (c) 392 (d) 471
  11. 11.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 16 (b) 17 (c) 18 (d) 6
  13. 13.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
  14. 14.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  15. 15.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 150 (c) 159 (d) 160
  16. 16.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) 18 (d) 162
  17. 17.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  18. 18.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 167 (b) 158 (c) 168 (d) 176
  19. 19.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 51 (b) 42 (c) 60 (d) 52
  20. 20.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 544 (b) 434 (c) 543 (d) 534
  21. 21.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) 117 (b) 39 (c) 42 (d) 13
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 18 (b) 20 (c) 9 (d) 19
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 15 (b) 5 (c) 17 (d) 16
  24. 24.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 396 (c) 342 (d) 406
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 95? (a) 20 (b) 18 (c) 9 (d) 19
  26. 26.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) 21 (b) 18 (c) 6 (d) 54
  27. 27.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  28. 28.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 409 (c) 408 (d) 344
  29. 29.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
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 6 (b) 4 (c) 3 (d) 5
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 4 (d) 5
  32. 32.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 181 (b) 190 (c) 172 (d) 182
  33. 33.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 26 (b) 36 (c) 35 (d) 44
  34. 34.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 7 (d) 8
  35. 35.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) 72 (b) 24 (c) 8 (d) 27
  36. 36.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 45 (c) 15 (d) 18
  37. 37.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 475 (c) 474 (d) 465
  38. 38.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 427 (b) 417 (c) 356 (d) 426
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 14 (d) 15
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 63? (a) 11 (b) 6 (c) 10 (d) 8

Answer key

  1. 4
  2. 6
  3. 72
  4. 6
  5. 8
  6. 16
  7. 42
  8. 45
  9. 624
  10. 480
  11. 5
  12. 17
  13. 9
  14. 9
  15. 159
  16. 54
  17. 5
  18. 167
  19. 51
  20. 543
  21. 39
  22. 19
  23. 16
  24. 405
  25. 19
  26. 18
  27. 4
  28. 408
  29. 69
  30. 5
  31. 5
  32. 181
  33. 35
  34. 7
  35. 24
  36. 15
  37. 474
  38. 426
  39. 15
  40. 10

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