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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 177 · 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 12? (a) 6 (b) 8 (c) 13 (d) 7
  2. 2.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 66 (c) 56 (d) 65
  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) 5 (b) 15 (c) 45 (d) 18
  4. 4.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 400 (c) 492 (d) 493
  5. 5.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
  6. 6.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) 126 (c) 45 (d) 42
  7. 7.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
  8. 8.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 14 (b) 15 (c) 13 (d) 4
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 4 (b) 14 (c) 15 (d) 16
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 10 (b) 12 (c) 11 (d) 3
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 8 (b) 6 (c) 7 (d) 5
  13. 13.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) 48 (c) 144 (d) 51
  14. 14.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 546 (c) 556 (d) 555
  15. 15.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 18 (b) 7 (c) 16 (d) 17
  17. 17.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) 21 (b) 54 (c) 6 (d) 18
  18. 18.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 46 (c) 56 (d) 55
  19. 19.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 286 (c) 322 (d) 321
  20. 20.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 13 (b) 14 (c) 15 (d) 3
  22. 22.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
  23. 23.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) 69 (b) 23 (c) 207 (d) 72
  24. 24.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) 60 (c) 171 (d) 19
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 4 (b) 6 (c) 5 (d) 3
  26. 26.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 109 (c) 118 (d) 110
  27. 27.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) 51 (b) 54 (c) 153 (d) 17
  28. 28.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 343 (c) 342 (d) 333
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 5 (b) 3 (c) 4 (d) 2
  30. 30.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  31. 31.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 80? (a) 8 (b) 7 (c) 9 (d) 6
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 15 (b) 5 (c) 17 (d) 16
  34. 34.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) 66 (b) 189 (c) 63 (d) 21
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 14 (b) 15 (c) 16 (d) 5
  36. 36.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 128 (c) 138 (d) 137
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 14 (b) 16 (c) 15 (d) 5
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 18 (b) 6 (c) 16 (d) 17
  39. 39.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 105 (c) 106 (d) 96
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 8 (d) 18

Answer key

  1. 7
  2. 65
  3. 15
  4. 492
  5. 9
  6. 42
  7. 45
  8. 2
  9. 14
  10. 15
  11. 11
  12. 7
  13. 48
  14. 555
  15. 9
  16. 17
  17. 18
  18. 55
  19. 321
  20. 2
  21. 14
  22. 4
  23. 69
  24. 57
  25. 5
  26. 109
  27. 51
  28. 342
  29. 4
  30. 8
  31. 4
  32. 8
  33. 16
  34. 63
  35. 15
  36. 137
  37. 15
  38. 17
  39. 105
  40. 18

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