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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 983 · 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 48? (a) 4 (b) 3 (c) 5 (d) 6
  2. 2.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) 18 (b) 5 (c) 15 (d) 45
  3. 3.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 616 (c) 606 (d) 482
  4. 4.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  5. 5.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) 162 (c) 172 (d) 171
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 2 (b) 4 (c) 3 (d) 5
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 10 (b) 8 (c) 11 (d) 9
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 67? (a) 4 (b) 6 (c) 7 (d) 5
  9. 9.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) 24 (b) 216 (c) 75 (d) 72
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 9 (b) 20 (c) 21 (d) 19
  11. 11.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  12. 12.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 397 (c) 336 (d) 387
  13. 13.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) 23 (b) 72 (c) 69 (d) 207
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 2 (b) 1 (c) 4 (d) 3
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 1 (b) 3 (c) 4 (d) 2
  16. 16.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) 57 (c) 60 (d) 171
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 20 (b) 18 (c) 9 (d) 19
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 3 (b) 13 (c) 15 (d) 14
  19. 19.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 24 (c) 34 (d) 33
  20. 20.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) 144 (c) 51 (d) 48
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 19 (b) 18 (c) 17 (d) 7
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 5 (b) 3 (c) 4 (d) 2
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 59? (a) 16 (b) 17 (c) 15 (d) 5
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 4 (b) 3 (c) 2 (d) 5
  25. 25.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 55 (b) 56 (c) 46 (d) 64
  26. 26.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 152 (c) 143 (d) 134
  27. 27.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 122 (c) 140 (d) 131
  28. 28.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 10 (d) 2
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 16 (b) 4 (c) 15 (d) 14
  30. 30.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) 63 (b) 24 (c) 21 (d) 7
  31. 31.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 18 (d) 1
  32. 32.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 292 (c) 266 (d) 291
  33. 33.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 150 (c) 159 (d) 160
  34. 34.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 4 (b) 2 (c) 3 (d) 5
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 64? (a) 18 (b) 16 (c) 17 (d) 6
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 70? (a) 7 (b) 17 (c) 16 (d) 18
  38. 38.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) 63 (c) 60 (d) 180
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 90? (a) 9 (b) 18 (c) 20 (d) 19
  40. 40.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5

Answer key

  1. 5
  2. 15
  3. 615
  4. 9
  5. 171
  6. 4
  7. 10
  8. 6
  9. 72
  10. 20
  11. 5
  12. 396
  13. 69
  14. 3
  15. 3
  16. 57
  17. 19
  18. 14
  19. 33
  20. 48
  21. 18
  22. 4
  23. 16
  24. 4
  25. 55
  26. 143
  27. 131
  28. 3
  29. 15
  30. 21
  31. 2
  32. 291
  33. 159
  34. 6
  35. 4
  36. 17
  37. 17
  38. 60
  39. 19
  40. 4

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