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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 379 · 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 times is the digit 6 written when you write all the numbers from 1 to 41? (a) 4 (b) 2 (c) 3 (d) 5
  2. 2.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  3. 3.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 70 (c) 61 (d) 52
  4. 4.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) 51 (b) 16 (c) 48 (d) 144
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 18 (b) 8 (c) 17 (d) 19
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 44? (a) 3 (b) 2 (c) 5 (d) 4
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 5 (d) 3
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 2 (b) 3 (c) 1 (d) 4
  9. 9.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
  10. 10.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) 24 (c) 21 (d) 63
  11. 11.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 2 (d) 1
  12. 12.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) 18 (b) 6 (c) 21 (d) 54
  13. 13.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 46 (c) 36 (d) 45
  14. 14.The numbers 7 to 15 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) 11 (c) 36 (d) 99
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 18 (b) 17 (c) 6 (d) 16
  16. 16.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
  17. 17.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) 8 (b) 27 (c) 72 (d) 24
  18. 18.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 368 (b) 435 (c) 445 (d) 444
  19. 19.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 362 (c) 426 (d) 436
  20. 20.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) 51 (b) 54 (c) 153 (d) 17
  21. 21.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 165 (c) 166 (d) 156
  22. 22.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) 162 (d) 18
  23. 23.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 60 (c) 57 (d) 171
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 81? (a) 17 (b) 18 (c) 19 (d) 8
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 17 (b) 19 (c) 18 (d) 7
  26. 26.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 4 (b) 3 (c) 2 (d) 5
  28. 28.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) 189 (b) 21 (c) 63 (d) 66
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 5 (b) 14 (c) 15 (d) 16
  30. 30.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 6 (d) 13
  31. 31.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) 10 (b) 33 (c) 30 (d) 90
  32. 32.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 66 (c) 58 (d) 57
  33. 33.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 160 (c) 142 (d) 151
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 7 (b) 17 (c) 16 (d) 18
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 93? (a) 9 (b) 20 (c) 19 (d) 18
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 99? (a) 9 (b) 21 (c) 19 (d) 20
  37. 37.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
  38. 38.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 604 (b) 594 (c) 474 (d) 603
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 16 (b) 15 (c) 5 (d) 17
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 20 (b) 19 (c) 9 (d) 18

Answer key

  1. 4
  2. 3
  3. 61
  4. 48
  5. 18
  6. 4
  7. 4
  8. 3
  9. 5
  10. 21
  11. 2
  12. 18
  13. 45
  14. 33
  15. 17
  16. 2
  17. 24
  18. 444
  19. 435
  20. 51
  21. 165
  22. 54
  23. 57
  24. 18
  25. 18
  26. 7
  27. 4
  28. 63
  29. 15
  30. 7
  31. 30
  32. 57
  33. 151
  34. 17
  35. 19
  36. 20
  37. 4
  38. 603
  39. 16
  40. 19

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