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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 609 · 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.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 225 (b) 222 (c) 216 (d) 226
  2. 2.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) 171 (b) 57 (c) 60 (d) 19
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 15 (b) 14 (c) 13 (d) 4
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 11 (b) 10 (c) 12 (d) 4
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  6. 6.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) 10 (b) 33 (c) 30 (d) 90
  7. 7.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
  8. 8.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) 18 (b) 21 (c) 54 (d) 6
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 5 (b) 4 (c) 3 (d) 6
  10. 10.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) 48 (b) 144 (c) 16 (d) 51
  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) 27 (b) 72 (c) 8 (d) 24
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 18 (b) 7 (c) 16 (d) 17
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 91? (a) 11 (b) 10 (c) 12 (d) 9
  14. 14.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 204 (c) 205 (d) 208
  15. 15.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) 7 (b) 21 (c) 24 (d) 63
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 17 (b) 19 (c) 18 (d) 8
  17. 17.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 18 (d) 1
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 90? (a) 18 (b) 9 (c) 20 (d) 19
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 17 (b) 18 (c) 19 (d) 7
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 20 (b) 18 (c) 9 (d) 19
  21. 21.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 240 (c) 232 (d) 241
  22. 22.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) 131 (c) 140 (d) 122
  23. 23.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
  24. 24.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  25. 25.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 8 (b) 7 (c) 6 (d) 5
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 67? (a) 5 (b) 6 (c) 8 (d) 7
  28. 28.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) 27 (b) 9 (c) 81 (d) 30
  29. 29.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 230 (b) 228 (c) 238 (d) 237
  30. 30.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 236 (c) 246 (d) 247
  31. 31.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 24 (b) 34 (c) 42 (d) 33
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 7 (b) 4 (c) 6 (d) 5
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 2 (b) 3 (c) 4 (d) 1
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 19 (b) 20 (c) 9 (d) 21
  35. 35.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 6 (b) 16 (c) 17 (d) 18
  37. 37.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  38. 38.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) 118 (c) 136 (d) 128
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 8 (b) 17 (c) 18 (d) 19
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 81? (a) 18 (b) 19 (c) 17 (d) 8

Answer key

  1. 225
  2. 57
  3. 14
  4. 11
  5. 6
  6. 30
  7. 3
  8. 18
  9. 5
  10. 48
  11. 24
  12. 17
  13. 11
  14. 204
  15. 21
  16. 18
  17. 2
  18. 19
  19. 18
  20. 19
  21. 240
  22. 131
  23. 5
  24. 4
  25. 5
  26. 7
  27. 7
  28. 27
  29. 237
  30. 246
  31. 33
  32. 6
  33. 3
  34. 20
  35. 9
  36. 17
  37. 3
  38. 127
  39. 18
  40. 18

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