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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 790 · 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 17? (a) 18 (b) 3 (c) 2 (d) 1
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 18 (b) 17 (c) 6 (d) 16
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 9 (b) 19 (c) 20 (d) 18
  4. 4.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 5 (b) 6 (c) 8 (d) 7
  6. 6.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) 45 (c) 42 (d) 14
  7. 7.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 1 (b) 4 (c) 2 (d) 3
  9. 9.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) 12 (b) 108 (c) 39 (d) 36
  10. 10.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 267 (c) 277 (d) 256
  11. 11.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 622 (c) 612 (d) 621
  12. 12.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 206 (c) 201 (d) 202
  13. 13.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 86 (c) 77 (d) 78
  14. 14.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 249 (c) 240 (d) 238
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 15 (b) 16 (c) 17 (d) 5
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 3 (b) 6 (c) 4 (d) 5
  17. 17.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 476 (b) 597 (c) 607 (d) 606
  18. 18.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  19. 19.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 205 (c) 208 (d) 195
  20. 20.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 8 (d) 11
  21. 21.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) 48 (c) 16 (d) 51
  22. 22.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) 63 (b) 21 (c) 24 (d) 7
  23. 23.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
  24. 24.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
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 86? (a) 9 (b) 8 (c) 7 (d) 6
  26. 26.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 64 (c) 73 (d) 82
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 14 (b) 5 (c) 15 (d) 16
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 99? (a) 20 (b) 9 (c) 19 (d) 21
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 5 (b) 6 (c) 4 (d) 7
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 6 (b) 7 (c) 5 (d) 8
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 16 (b) 14 (c) 4 (d) 15
  32. 32.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 222 (c) 225 (d) 216
  33. 33.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 573 (c) 574 (d) 564
  34. 34.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 111 (c) 102 (d) 112
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 15 (b) 16 (c) 4 (d) 14
  36. 36.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 633 (c) 634 (d) 494
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 12 (b) 3 (c) 14 (d) 13
  38. 38.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 138 (c) 120 (d) 129
  39. 39.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 55 (c) 64 (d) 56
  40. 40.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 343 (c) 342 (d) 333

Answer key

  1. 2
  2. 17
  3. 19
  4. 3
  5. 7
  6. 42
  7. 3
  8. 3
  9. 36
  10. 276
  11. 621
  12. 201
  13. 77
  14. 249
  15. 16
  16. 5
  17. 606
  18. 8
  19. 204
  20. 9
  21. 48
  22. 21
  23. 5
  24. 57
  25. 8
  26. 73
  27. 15
  28. 20
  29. 6
  30. 7
  31. 15
  32. 225
  33. 573
  34. 111
  35. 15
  36. 633
  37. 13
  38. 129
  39. 55
  40. 342

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