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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 176 · 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 14? (a) 15 (b) 6 (c) 4 (d) 5
  2. 2.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 224 (c) 228 (d) 229
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 9 (b) 20 (c) 21 (d) 19
  4. 4.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 9 (b) 27 (c) 30 (d) 81
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 18 (b) 6 (c) 17 (d) 16
  6. 6.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 10 (d) 11
  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) 48 (b) 45 (c) 135 (d) 15
  8. 8.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  9. 9.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 151 (c) 142 (d) 160
  10. 10.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 570 (c) 571 (d) 452
  11. 11.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  12. 12.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) 72 (b) 75 (c) 24 (d) 216
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 16 (b) 5 (c) 14 (d) 15
  14. 14.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 483 (c) 400 (d) 493
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 73? (a) 16 (b) 17 (c) 18 (d) 7
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 8 (b) 17 (c) 18 (d) 19
  17. 17.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) 72 (c) 8 (d) 27
  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) 51 (c) 17 (d) 153
  19. 19.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) 162 (b) 54 (c) 18 (d) 57
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 9 (b) 20 (c) 19 (d) 21
  21. 21.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 10 (d) 9
  22. 22.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 127 (b) 136 (c) 118 (d) 128
  23. 23.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 286 (c) 262 (d) 285
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 6 (b) 4 (c) 3 (d) 5
  25. 25.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
  26. 26.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  27. 27.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) 60 (b) 180 (c) 63 (d) 20
  28. 28.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 5 (d) 3
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 19 (b) 21 (c) 20 (d) 9
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 18 (b) 19 (c) 20 (d) 8
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 17 (b) 16 (c) 6 (d) 15
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 91? (a) 9 (b) 18 (c) 19 (d) 20
  33. 33.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) 11 (d) 33
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 13 (b) 14 (c) 11 (d) 9
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 18 (b) 19 (c) 17 (d) 7
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 3 (b) 4 (c) 2 (d) 1
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 20 (b) 19 (c) 18 (d) 8
  38. 38.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  39. 39.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) 6 (b) 54 (c) 21 (d) 18
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 6 (b) 18 (c) 16 (d) 17

Answer key

  1. 5
  2. 228
  3. 20
  4. 27
  5. 17
  6. 9
  7. 45
  8. 4
  9. 151
  10. 570
  11. 7
  12. 72
  13. 15
  14. 492
  15. 17
  16. 18
  17. 24
  18. 51
  19. 54
  20. 20
  21. 8
  22. 127
  23. 285
  24. 5
  25. 2
  26. 5
  27. 60
  28. 4
  29. 20
  30. 19
  31. 16
  32. 19
  33. 33
  34. 13
  35. 18
  36. 3
  37. 19
  38. 9
  39. 18
  40. 17

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