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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 207 · 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 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) 39 (c) 12 (d) 36
  2. 2.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) 189 (b) 21 (c) 63 (d) 66
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 9 (b) 13 (c) 15 (d) 16
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 14 (b) 4 (c) 15 (d) 16
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 18 (b) 8 (c) 17 (d) 19
  6. 6.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 6 (d) 13
  7. 7.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  8. 8.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 5 (d) 7
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 81? (a) 19 (b) 17 (c) 8 (d) 18
  10. 10.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  11. 11.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 328 (c) 327 (d) 290
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 17 (b) 18 (c) 7 (d) 19
  13. 13.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 104 (c) 95 (d) 86
  14. 14.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 84 (c) 75 (d) 76
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 2 (b) 1 (c) 4 (d) 3
  16. 16.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 156 (c) 164 (d) 155
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 3 (b) 5 (c) 6 (d) 4
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 2 (b) 3 (c) 4 (d) 5
  19. 19.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 312 (c) 313 (d) 303
  20. 20.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 418 (c) 519 (d) 520
  21. 21.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) 99 (b) 11 (c) 36 (d) 33
  22. 22.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  23. 23.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 154 (c) 163 (d) 172
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 76? (a) 6 (b) 7 (c) 8 (d) 5
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 14 (b) 16 (c) 15 (d) 4
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 3 (b) 4 (c) 5 (d) 2
  27. 27.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 577 (b) 567 (c) 576 (d) 456
  28. 28.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) 49 (c) 50 (d) 40
  29. 29.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 586 (c) 462 (d) 576
  30. 30.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 53 (c) 44 (d) 54
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 19 (d) 20
  32. 32.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 204 (c) 205 (d) 195
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 14 (b) 16 (c) 4 (d) 15
  34. 34.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) 352 (c) 351 (d) 342
  35. 35.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 90 (c) 99 (d) 100
  36. 36.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
  37. 37.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
  38. 38.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 318 (c) 369 (d) 370
  39. 39.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 10 (c) 33 (d) 30
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 15 (b) 16 (c) 14 (d) 5

Answer key

  1. 36
  2. 63
  3. 15
  4. 15
  5. 18
  6. 7
  7. 3
  8. 6
  9. 18
  10. 4
  11. 327
  12. 18
  13. 95
  14. 75
  15. 3
  16. 155
  17. 5
  18. 4
  19. 312
  20. 519
  21. 33
  22. 2
  23. 163
  24. 7
  25. 15
  26. 4
  27. 576
  28. 49
  29. 585
  30. 53
  31. 19
  32. 204
  33. 15
  34. 351
  35. 99
  36. 6
  37. 2
  38. 369
  39. 30
  40. 15

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