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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 655 · 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) 4 (b) 3 (c) 2 (d) 10
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 8 (b) 18 (c) 19 (d) 20
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 3 (b) 4 (c) 2 (d) 1
  4. 4.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) 189 (c) 21 (d) 63
  5. 5.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) 90 (c) 10 (d) 33
  6. 6.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) 60 (c) 20 (d) 63
  7. 7.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 260 (b) 273 (c) 283 (d) 282
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 4 (b) 3 (c) 2 (d) 1
  9. 9.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) 8 (c) 72 (d) 24
  10. 10.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) 22 (b) 198 (c) 69 (d) 66
  11. 11.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) 5 (c) 18 (d) 45
  12. 12.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) 36 (b) 12 (c) 39 (d) 108
  13. 13.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 9 (b) 30 (c) 27 (d) 81
  14. 14.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 508 (b) 410 (c) 507 (d) 498
  15. 15.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 538 (b) 528 (c) 537 (d) 430
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 5 (b) 6 (c) 4 (d) 7
  17. 17.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 2 (d) 1
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 97? (a) 18 (b) 9 (c) 19 (d) 20
  19. 19.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 158 (c) 149 (d) 140
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 14 (d) 15
  21. 21.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 81 (c) 72 (d) 82
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 4 (b) 2 (c) 5 (d) 3
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 17 (b) 18 (c) 19 (d) 8
  24. 24.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  25. 25.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) 21 (b) 6 (c) 54 (d) 18
  26. 26.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) 112 (c) 103 (d) 94
  27. 27.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 285 (c) 295 (d) 268
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 13 (b) 15 (c) 4 (d) 14
  29. 29.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 68? (a) 16 (b) 17 (c) 6 (d) 15
  31. 31.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) 370 (c) 369 (d) 318
  32. 32.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 68? (a) 8 (b) 5 (c) 6 (d) 7
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 19 (b) 9 (c) 20 (d) 21
  35. 35.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 52 (c) 42 (d) 51
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 19 (b) 21 (c) 20 (d) 9
  37. 37.The numbers 11 to 19 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) 135 (c) 48 (d) 45
  38. 38.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) 21 (c) 63 (d) 24
  39. 39.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 14 (b) 16 (c) 5 (d) 15

Answer key

  1. 3
  2. 19
  3. 3
  4. 63
  5. 30
  6. 60
  7. 282
  8. 3
  9. 24
  10. 66
  11. 15
  12. 36
  13. 27
  14. 507
  15. 537
  16. 6
  17. 2
  18. 19
  19. 149
  20. 15
  21. 81
  22. 4
  23. 18
  24. 4
  25. 18
  26. 103
  27. 294
  28. 14
  29. 4
  30. 16
  31. 369
  32. 5
  33. 7
  34. 20
  35. 51
  36. 20
  37. 45
  38. 21
  39. 9
  40. 15

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