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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 372 · 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 10? (a) 8 (b) 10 (c) 9 (d) 11
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 18 (d) 8
  3. 3.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 235 (b) 225 (c) 228 (d) 234
  4. 4.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 81? (a) 8 (b) 19 (c) 18 (d) 17
  6. 6.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) 290 (c) 328 (d) 327
  7. 7.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 432 (c) 540 (d) 541
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 70? (a) 8 (b) 5 (c) 6 (d) 7
  9. 9.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 3 (d) 2
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 3 (b) 13 (c) 15 (d) 14
  11. 11.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) 42 (c) 14 (d) 45
  12. 12.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 9 (b) 10 (c) 7 (d) 8
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 19 (b) 8 (c) 17 (d) 18
  15. 15.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) 66 (b) 21 (c) 189 (d) 63
  16. 16.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) 15 (b) 45 (c) 5 (d) 18
  17. 17.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 567 (c) 558 (d) 568
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 16 (b) 14 (c) 4 (d) 15
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 14 (b) 4 (c) 15 (d) 16
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 19 (b) 18 (c) 17 (d) 8
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 68? (a) 6 (b) 5 (c) 7 (d) 8
  22. 22.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 202 (b) 195 (c) 186 (d) 196
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 8 (b) 7 (c) 6 (d) 5
  24. 24.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 32 (c) 50 (d) 41
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 6 (b) 3 (c) 4 (d) 5
  26. 26.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 84 (c) 75 (d) 66
  27. 27.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 288 (c) 324 (d) 325
  28. 28.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  29. 29.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  30. 30.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
  31. 31.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) 27 (b) 72 (c) 8 (d) 24
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 53? (a) 6 (b) 5 (c) 3 (d) 4
  33. 33.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) 7 (d) 24
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 17 (b) 18 (c) 7 (d) 19
  35. 35.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 10 (d) 6
  36. 36.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 510 (c) 520 (d) 519
  37. 37.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) 24 (b) 216 (c) 75 (d) 72
  38. 38.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 165 (b) 174 (c) 166 (d) 156
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 15 (b) 14 (c) 3 (d) 13
  40. 40.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) 39 (b) 36 (c) 108 (d) 12

Answer key

  1. 9
  2. 18
  3. 234
  4. 3
  5. 18
  6. 327
  7. 540
  8. 7
  9. 2
  10. 14
  11. 42
  12. 7
  13. 9
  14. 18
  15. 63
  16. 15
  17. 567
  18. 15
  19. 15
  20. 18
  21. 7
  22. 195
  23. 7
  24. 41
  25. 5
  26. 75
  27. 324
  28. 2
  29. 6
  30. 4
  31. 24
  32. 5
  33. 21
  34. 18
  35. 7
  36. 519
  37. 72
  38. 165
  39. 14
  40. 36

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