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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 428 · 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 3? (a) 2 (b) 4 (c) 10 (d) 3
  2. 2.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 49 (b) 50 (c) 58 (d) 40
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 17 (b) 15 (c) 16 (d) 5
  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) 14 (c) 45 (d) 42
  5. 5.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  6. 6.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
  7. 7.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 151 (b) 160 (c) 152 (d) 142
  8. 8.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 213 (b) 220 (c) 222 (d) 223
  9. 9.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 99? (a) 21 (b) 19 (c) 20 (d) 9
  11. 11.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 103 (c) 112 (d) 94
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 6 (b) 4 (c) 5 (d) 3
  14. 14.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 434 (b) 544 (c) 543 (d) 534
  15. 15.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 267 (b) 250 (c) 258 (d) 268
  16. 16.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 423 (c) 433 (d) 432
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 4 (b) 3 (c) 2 (d) 1
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 15 (b) 16 (c) 17 (d) 5
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 44? (a) 5 (b) 3 (c) 2 (d) 4
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 94? (a) 15 (b) 12 (c) 14 (d) 9
  21. 21.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 153 (b) 17 (c) 51 (d) 54
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 4 (b) 1 (c) 2 (d) 3
  23. 23.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 595 (c) 594 (d) 468
  24. 24.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 16 (b) 15 (c) 5 (d) 17
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 7 (b) 6 (c) 5 (d) 4
  27. 27.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 20 (b) 19 (c) 21 (d) 9
  29. 29.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 456 (c) 457 (d) 376
  30. 30.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 592 (c) 582 (d) 466
  31. 31.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
  32. 32.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) 33 (b) 90 (c) 10 (d) 30
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 8 (b) 18 (c) 20 (d) 19
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 58? (a) 4 (b) 3 (c) 5 (d) 6
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 2 (b) 3 (c) 4 (d) 5
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 18 (b) 17 (c) 16 (d) 6
  37. 37.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 7 (d) 10
  38. 38.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 13 (b) 11 (c) 12 (d) 5
  40. 40.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7

Answer key

  1. 3
  2. 49
  3. 16
  4. 42
  5. 5
  6. 9
  7. 151
  8. 222
  9. 5
  10. 20
  11. 103
  12. 9
  13. 5
  14. 543
  15. 267
  16. 432
  17. 3
  18. 16
  19. 4
  20. 14
  21. 51
  22. 3
  23. 594
  24. 2
  25. 16
  26. 6
  27. 4
  28. 20
  29. 456
  30. 591
  31. 54
  32. 30
  33. 19
  34. 5
  35. 4
  36. 17
  37. 6
  38. 2
  39. 12
  40. 7

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