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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 879 · 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 3 written when you write all the numbers from 1 to 59? (a) 15 (b) 16 (c) 5 (d) 17
  2. 2.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) 63 (b) 21 (c) 66 (d) 189
  3. 3.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 16 (d) 3
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 5 (b) 16 (c) 15 (d) 17
  5. 5.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7
  6. 6.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) 54 (b) 17 (c) 51 (d) 153
  7. 7.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 37 (c) 28 (d) 38
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 19 (b) 9 (c) 21 (d) 20
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 5 (b) 8 (c) 7 (d) 6
  10. 10.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 117 (c) 126 (d) 108
  11. 11.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) 36 (c) 11 (d) 99
  12. 12.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 112 (c) 111 (d) 102
  13. 13.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
  14. 14.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) 72 (b) 8 (c) 27 (d) 24
  15. 15.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) 216 (b) 24 (c) 75 (d) 72
  16. 16.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 181 (b) 182 (c) 172 (d) 190
  17. 17.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) 45 (b) 15 (c) 135 (d) 48
  18. 18.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 64? (a) 17 (b) 16 (c) 6 (d) 18
  20. 20.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 8 (d) 7
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 18 (d) 19
  22. 22.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
  23. 23.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
  24. 24.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 10 (d) 8
  25. 25.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 23 (c) 72 (d) 69
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 2 (b) 4 (c) 5 (d) 3
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 3 (b) 1 (c) 2 (d) 4
  28. 28.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 7 (b) 5 (c) 6 (d) 4
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 80? (a) 6 (b) 8 (c) 7 (d) 9
  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) 90 (b) 30 (c) 10 (d) 33
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 15 (b) 17 (c) 16 (d) 5
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 18 (b) 17 (c) 19 (d) 8
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 17 (b) 15 (c) 16 (d) 5
  35. 35.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 4 (d) 6
  36. 36.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 312 (c) 361 (d) 351
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 18 (b) 8 (c) 20 (d) 19
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 2 (b) 3 (c) 4 (d) 1
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 40? (a) 5 (b) 3 (c) 2 (d) 4
  40. 40.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 355 (b) 345 (c) 354 (d) 308

Answer key

  1. 16
  2. 63
  3. 4
  4. 16
  5. 6
  6. 51
  7. 37
  8. 20
  9. 7
  10. 117
  11. 33
  12. 111
  13. 60
  14. 24
  15. 72
  16. 181
  17. 45
  18. 7
  19. 17
  20. 7
  21. 18
  22. 4
  23. 36
  24. 9
  25. 69
  26. 4
  27. 3
  28. 3
  29. 6
  30. 8
  31. 30
  32. 16
  33. 18
  34. 16
  35. 5
  36. 360
  37. 19
  38. 3
  39. 4
  40. 354

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