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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 49 · 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 2? (a) 1 (b) 2 (c) 3 (d) 10
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 16 (b) 15 (c) 14 (d) 4
  3. 3.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
  4. 4.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) 14 (d) 42
  5. 5.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) 7 (b) 63 (c) 24 (d) 21
  6. 6.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 59 (c) 50 (d) 60
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 19 (d) 18
  8. 8.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 586 (b) 462 (c) 585 (d) 576
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 5 (b) 4 (c) 3 (d) 2
  10. 10.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) 24 (b) 8 (c) 27 (d) 72
  11. 11.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) 18 (b) 162 (c) 54 (d) 57
  12. 12.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) 60 (d) 63
  13. 13.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 225 (b) 235 (c) 234 (d) 228
  14. 14.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 10 (d) 9
  15. 15.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 4 (d) 6
  16. 16.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 478 (b) 468 (c) 390 (d) 477
  17. 17.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 5 (b) 17 (c) 16 (d) 15
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 3 (b) 2 (c) 4 (d) 1
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 3 (b) 4 (c) 2 (d) 1
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 15 (b) 5 (c) 16 (d) 17
  22. 22.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 144 (c) 126 (d) 135
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 4 (b) 14 (c) 13 (d) 15
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 3 (b) 2 (c) 1 (d) 4
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 4 (b) 1 (c) 3 (d) 2
  26. 26.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 11 (d) 8
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 19 (b) 18 (c) 17 (d) 7
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 19 (b) 8 (c) 17 (d) 18
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 5 (b) 6 (c) 7 (d) 8
  30. 30.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) 30 (b) 10 (c) 33 (d) 90
  31. 31.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 342 (c) 343 (d) 300
  32. 32.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 3 (d) 2
  33. 33.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  34. 34.The numbers 18 to 26 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) 22 (c) 69 (d) 198
  35. 35.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 592 (c) 582 (d) 591
  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) 633 (b) 494 (c) 634 (d) 624
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 62? (a) 7 (b) 4 (c) 5 (d) 6
  38. 38.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 309 (b) 319 (c) 318 (d) 284
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 80? (a) 8 (b) 7 (c) 9 (d) 10
  40. 40.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6

Answer key

  1. 2
  2. 15
  3. 3
  4. 42
  5. 21
  6. 59
  7. 19
  8. 585
  9. 4
  10. 24
  11. 54
  12. 60
  13. 234
  14. 8
  15. 5
  16. 477
  17. 5
  18. 16
  19. 3
  20. 3
  21. 16
  22. 135
  23. 14
  24. 3
  25. 3
  26. 9
  27. 18
  28. 18
  29. 7
  30. 30
  31. 342
  32. 2
  33. 7
  34. 66
  35. 591
  36. 633
  37. 6
  38. 318
  39. 9
  40. 6

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