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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 446 · 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 8 to 16 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) 12 (c) 108 (d) 39
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 17 (b) 19 (c) 18 (d) 7
  3. 3.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 441 (c) 451 (d) 372
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 14 (b) 13 (c) 12 (d) 3
  5. 5.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 550 (b) 540 (c) 549 (d) 438
  6. 6.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 9 (d) 11
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 5 (b) 2 (c) 4 (d) 3
  8. 8.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
  9. 9.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) 45 (b) 126 (c) 42 (d) 14
  10. 10.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) 171 (c) 57 (d) 60
  11. 11.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) 72 (b) 24 (c) 8 (d) 27
  12. 12.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) 18 (c) 5 (d) 45
  13. 13.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 119 (c) 110 (d) 120
  14. 14.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 123 (c) 114 (d) 124
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 7 (b) 3 (c) 4 (d) 6
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 3 (b) 13 (c) 15 (d) 14
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 5 (b) 4 (c) 2 (d) 3
  18. 18.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) 54 (b) 17 (c) 153 (d) 51
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 92? (a) 9 (b) 18 (c) 19 (d) 20
  20. 20.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 8 (d) 13
  21. 21.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 9 (d) 7
  22. 22.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 2 (d) 3
  23. 23.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) 30 (b) 90 (c) 33 (d) 10
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 14 (b) 16 (c) 15 (d) 4
  25. 25.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) 216 (b) 24 (c) 72 (d) 75
  26. 26.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 4 (d) 6
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 3 (b) 4 (c) 6 (d) 5
  28. 28.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 30 (c) 39 (d) 40
  29. 29.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) 15 (c) 135 (d) 45
  30. 30.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) 144 (b) 16 (c) 48 (d) 51
  31. 31.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 224 (b) 228 (c) 229 (d) 219
  32. 32.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 541 (b) 432 (c) 540 (d) 531
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 2 (b) 1 (c) 4 (d) 3
  34. 34.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 168 (c) 150 (d) 159
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 18 (b) 16 (c) 6 (d) 17
  36. 36.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 222 (c) 216 (d) 225
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 10 (b) 12 (c) 13 (d) 9
  38. 38.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 52 (c) 62 (d) 61
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 17 (b) 16 (c) 7 (d) 18
  40. 40.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 3 (d) 10

Answer key

  1. 36
  2. 18
  3. 450
  4. 13
  5. 549
  6. 9
  7. 4
  8. 2
  9. 42
  10. 57
  11. 24
  12. 15
  13. 119
  14. 123
  15. 6
  16. 14
  17. 4
  18. 51
  19. 19
  20. 7
  21. 8
  22. 2
  23. 30
  24. 15
  25. 72
  26. 5
  27. 5
  28. 39
  29. 45
  30. 48
  31. 228
  32. 540
  33. 3
  34. 159
  35. 17
  36. 225
  37. 12
  38. 61
  39. 17
  40. 4

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