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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 835 · 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 5 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 20 (d) 19
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 67? (a) 4 (b) 6 (c) 5 (d) 7
  3. 3.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) 45 (c) 5 (d) 18
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  5. 5.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
  6. 6.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) 135 (b) 15 (c) 48 (d) 45
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 19 (b) 20 (c) 9 (d) 18
  8. 8.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 39 (c) 42 (d) 117
  9. 9.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  10. 10.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) 99 (b) 36 (c) 33 (d) 11
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 19 (b) 7 (c) 18 (d) 17
  12. 12.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 171 (c) 162 (d) 172
  13. 13.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 426 (c) 435 (d) 362
  14. 14.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  15. 15.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 298 (c) 288 (d) 297
  16. 16.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  17. 17.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) 42 (b) 14 (c) 45 (d) 126
  18. 18.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
  19. 19.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
  20. 20.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 44 (c) 35 (d) 26
  21. 21.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 6 (d) 15
  22. 22.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 6 (b) 5 (c) 4 (d) 7
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 18 (b) 17 (c) 16 (d) 7
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 8 (b) 20 (c) 18 (d) 19
  26. 26.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 351 (c) 234 (d) 243
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
  28. 28.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) 72 (c) 69 (d) 23
  29. 29.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 58 (c) 67 (d) 76
  30. 30.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 173 (b) 164 (c) 182 (d) 174
  31. 31.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 92 (c) 82 (d) 91
  32. 32.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
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 2 (d) 3
  34. 34.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  35. 35.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 190 (c) 172 (d) 181
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 14 (b) 4 (c) 16 (d) 15
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 85? (a) 20 (b) 19 (c) 18 (d) 8
  38. 38.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) 57 (b) 171 (c) 19 (d) 60
  39. 39.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 206 (b) 192 (c) 201 (d) 202
  40. 40.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 616 (c) 482 (d) 615

Answer key

  1. 20
  2. 6
  3. 15
  4. 5
  5. 66
  6. 45
  7. 19
  8. 39
  9. 7
  10. 33
  11. 18
  12. 171
  13. 435
  14. 9
  15. 297
  16. 4
  17. 42
  18. 8
  19. 24
  20. 35
  21. 5
  22. 3
  23. 6
  24. 17
  25. 19
  26. 243
  27. 2
  28. 69
  29. 67
  30. 173
  31. 91
  32. 30
  33. 3
  34. 4
  35. 181
  36. 15
  37. 19
  38. 57
  39. 201
  40. 615

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