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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 839 · 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 4 written when you write all the numbers from 1 to 85? (a) 18 (b) 19 (c) 8 (d) 20
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 3 (b) 5 (c) 4 (d) 2
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 11 (b) 9 (c) 12 (d) 8
  4. 4.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  5. 5.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 2 (b) 1 (c) 3 (d) 4
  7. 7.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) 198 (c) 69 (d) 22
  8. 8.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) 66 (c) 21 (d) 63
  9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 19 (b) 18 (c) 9 (d) 20
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  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) 36 (b) 33 (c) 11 (d) 99
  12. 12.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 183 (b) 192 (c) 200 (d) 193
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 8 (b) 10 (c) 3 (d) 9
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 4 (b) 14 (c) 16 (d) 15
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 4 (b) 13 (c) 15 (d) 14
  16. 16.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) 223 (d) 222
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 15 (b) 16 (c) 5 (d) 17
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 4 (b) 3 (c) 2 (d) 1
  19. 19.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 19 (b) 20 (c) 8 (d) 18
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 14 (b) 16 (c) 4 (d) 15
  22. 22.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) 20 (b) 60 (c) 180 (d) 63
  23. 23.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 19 (b) 20 (c) 8 (d) 18
  25. 25.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 537 (b) 436 (c) 546 (d) 547
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 3 (b) 1 (c) 4 (d) 2
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 19 (b) 20 (c) 18 (d) 8
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 3 (d) 1
  29. 29.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) 5 (b) 45 (c) 18 (d) 15
  30. 30.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 340 (c) 393 (d) 403
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 5 (b) 15 (c) 16 (d) 14
  32. 32.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 14 (d) 7
  33. 33.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 244 (c) 243 (d) 234
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 49? (a) 3 (b) 5 (c) 6 (d) 4
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 5 (b) 6 (c) 7 (d) 4
  36. 36.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 475 (c) 474 (d) 388
  37. 37.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) 81 (b) 9 (c) 30 (d) 27
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 70? (a) 16 (b) 17 (c) 18 (d) 7
  39. 39.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) 75 (b) 72 (c) 24 (d) 216
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 3 (b) 5 (c) 2 (d) 4

Answer key

  1. 19
  2. 4
  3. 11
  4. 9
  5. 4
  6. 3
  7. 66
  8. 63
  9. 19
  10. 3
  11. 33
  12. 192
  13. 9
  14. 15
  15. 14
  16. 222
  17. 16
  18. 3
  19. 7
  20. 19
  21. 15
  22. 60
  23. 5
  24. 19
  25. 546
  26. 3
  27. 19
  28. 3
  29. 15
  30. 402
  31. 15
  32. 6
  33. 243
  34. 5
  35. 6
  36. 474
  37. 27
  38. 17
  39. 72
  40. 4

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