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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 939 · 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 6? (a) 10 (b) 7 (c) 5 (d) 6
  2. 2.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 16 (d) 3
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 9 (b) 20 (c) 18 (d) 19
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 3 (b) 2 (c) 1 (d) 4
  5. 5.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) 24 (b) 63 (c) 7 (d) 21
  6. 6.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 378 (c) 369 (d) 379
  7. 7.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  8. 8.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  9. 9.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) 171 (d) 57
  10. 10.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) 21 (b) 66 (c) 63 (d) 189
  11. 11.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) 6 (b) 54 (c) 18 (d) 21
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 46? (a) 4 (b) 5 (c) 3 (d) 2
  13. 13.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) 17 (b) 51 (c) 153 (d) 54
  14. 14.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 8 (b) 18 (c) 19 (d) 17
  16. 16.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 62 (c) 53 (d) 44
  17. 17.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  18. 18.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 416 (c) 516 (d) 517
  19. 19.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 174 (c) 182 (d) 173
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 18 (b) 20 (c) 19 (d) 8
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 68? (a) 5 (b) 4 (c) 7 (d) 6
  22. 22.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 5 (d) 14
  23. 23.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) 14 (b) 42 (c) 126 (d) 45
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 18 (b) 19 (c) 20 (d) 8
  25. 25.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 74 (c) 65 (d) 56
  26. 26.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) 57 (b) 18 (c) 162 (d) 54
  27. 27.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 532 (c) 531 (d) 426
  28. 28.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  29. 29.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  30. 30.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 615 (c) 488 (d) 625
  31. 31.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 340 (c) 298 (d) 339
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 21 (b) 20 (c) 19 (d) 9
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 1 (b) 2 (c) 3 (d) 4
  34. 34.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 172 (c) 180 (d) 171
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 16 (b) 14 (c) 4 (d) 15
  36. 36.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 6 (b) 17 (c) 16 (d) 18
  38. 38.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) 16 (b) 51 (c) 48 (d) 144
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 18 (b) 16 (c) 6 (d) 17
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 86? (a) 19 (b) 18 (c) 8 (d) 20

Answer key

  1. 6
  2. 4
  3. 19
  4. 3
  5. 21
  6. 378
  7. 9
  8. 2
  9. 57
  10. 63
  11. 18
  12. 4
  13. 51
  14. 9
  15. 18
  16. 53
  17. 3
  18. 516
  19. 173
  20. 19
  21. 6
  22. 6
  23. 42
  24. 19
  25. 65
  26. 54
  27. 531
  28. 3
  29. 8
  30. 624
  31. 339
  32. 20
  33. 3
  34. 171
  35. 15
  36. 4
  37. 17
  38. 48
  39. 17
  40. 19

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