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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 648 · 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 15? (a) 5 (b) 3 (c) 16 (d) 4
  2. 2.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
  3. 3.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  4. 4.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  5. 5.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 346 (c) 402 (d) 411
  6. 6.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) 72 (d) 24
  7. 7.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 570 (c) 579 (d) 580
  8. 8.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 410 (b) 498 (c) 507 (d) 508
  9. 9.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 337 (b) 327 (c) 296 (d) 336
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 2 (b) 4 (c) 3 (d) 5
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 13 (b) 15 (c) 14 (d) 3
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 3 (b) 5 (c) 6 (d) 4
  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) 54 (b) 57 (c) 18 (d) 162
  14. 14.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) 86 (c) 104 (d) 95
  15. 15.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 75 (c) 66 (d) 76
  16. 16.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 178 (c) 186 (d) 177
  17. 17.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 15 (b) 14 (c) 4 (d) 16
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 15 (b) 9 (c) 16 (d) 13
  20. 20.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 20 (c) 63 (d) 60
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 5 (b) 2 (c) 4 (d) 3
  22. 22.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 116 (c) 134 (d) 125
  23. 23.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
  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) 6 (b) 54 (c) 21 (d) 18
  25. 25.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 338 (c) 390 (d) 399
  26. 26.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 7 (b) 6 (c) 8 (d) 5
  28. 28.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
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 94? (a) 15 (b) 12 (c) 9 (d) 14
  30. 30.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 2 (d) 4
  31. 31.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 631 (c) 630 (d) 492
  32. 32.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 345 (c) 308 (d) 355
  33. 33.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
  34. 34.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 97 (c) 98 (d) 88
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 8 (b) 19 (c) 18 (d) 17
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 14 (b) 3 (c) 13 (d) 12
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 18 (b) 7 (c) 17 (d) 19
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 20 (b) 21 (c) 19 (d) 9
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 7 (b) 9 (c) 8 (d) 6
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 8 (b) 17 (c) 19 (d) 18

Answer key

  1. 4
  2. 7
  3. 3
  4. 6
  5. 411
  6. 72
  7. 579
  8. 507
  9. 336
  10. 4
  11. 14
  12. 5
  13. 54
  14. 95
  15. 75
  16. 177
  17. 8
  18. 15
  19. 15
  20. 60
  21. 4
  22. 125
  23. 2
  24. 18
  25. 399
  26. 2
  27. 7
  28. 48
  29. 14
  30. 3
  31. 630
  32. 354
  33. 4
  34. 97
  35. 18
  36. 13
  37. 18
  38. 20
  39. 8
  40. 18

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