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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 901 · 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.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) 45 (b) 15 (c) 18 (d) 5
  2. 2.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  3. 3.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 326 (c) 372 (d) 382
  4. 4.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) 42 (c) 39 (d) 117
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 2 (b) 4 (c) 1 (d) 3
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 44? (a) 2 (b) 5 (c) 4 (d) 3
  7. 7.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) 24 (b) 27 (c) 8 (d) 72
  8. 8.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 3 (d) 2
  9. 9.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 187 (c) 196 (d) 188
  10. 10.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  11. 11.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) 10 (c) 30 (d) 33
  12. 12.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 76 (c) 94 (d) 85
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 9 (b) 18 (c) 20 (d) 19
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 89? (a) 19 (b) 18 (c) 8 (d) 20
  15. 15.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  16. 16.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 7 (d) 5
  17. 17.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 8 (d) 19
  19. 19.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
  20. 20.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) 21 (c) 63 (d) 7
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 15 (b) 14 (c) 4 (d) 16
  22. 22.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) 82 (c) 92 (d) 91
  23. 23.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  24. 24.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
  25. 25.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) 198 (b) 66 (c) 69 (d) 22
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 9 (b) 21 (c) 20 (d) 19
  27. 27.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  28. 28.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) 48 (b) 45 (c) 15 (d) 135
  29. 29.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) 60 (b) 171 (c) 19 (d) 57
  30. 30.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 26 (b) 44 (c) 35 (d) 36
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 18 (b) 8 (c) 17 (d) 19
  32. 32.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 142 (c) 133 (d) 134
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 1 (b) 2 (c) 3 (d) 4
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 5 (b) 2 (c) 4 (d) 3
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 13 (b) 15 (c) 3 (d) 14
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 3 (b) 5 (c) 2 (d) 4
  37. 37.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
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 6 (b) 15 (c) 16 (d) 17
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 6 (b) 3 (c) 4 (d) 5
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 3 (b) 14 (c) 15 (d) 13

Answer key

  1. 15
  2. 5
  3. 381
  4. 39
  5. 3
  6. 4
  7. 24
  8. 2
  9. 187
  10. 4
  11. 30
  12. 85
  13. 19
  14. 19
  15. 2
  16. 6
  17. 8
  18. 19
  19. 131
  20. 21
  21. 15
  22. 91
  23. 4
  24. 33
  25. 66
  26. 20
  27. 9
  28. 45
  29. 57
  30. 35
  31. 18
  32. 133
  33. 3
  34. 4
  35. 14
  36. 4
  37. 54
  38. 16
  39. 5
  40. 14

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