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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 515 · 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 times is the digit 5 written when you write all the numbers from 1 to 58? (a) 5 (b) 14 (c) 15 (d) 16
  2. 2.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) 69 (b) 198 (c) 66 (d) 22
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 19 (b) 17 (c) 18 (d) 7
  4. 4.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  5. 5.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) 81 (c) 9 (d) 30
  6. 6.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 13 (b) 14 (c) 3 (d) 12
  8. 8.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) 17 (b) 153 (c) 51 (d) 54
  9. 9.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 43 (c) 44 (d) 34
  10. 10.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5
  11. 11.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) 54 (b) 21 (c) 6 (d) 18
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 6 (b) 8 (c) 5 (d) 7
  13. 13.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 180 (c) 189 (d) 190
  14. 14.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 50 (c) 41 (d) 42
  15. 15.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) 30 (c) 90 (d) 33
  16. 16.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 351 (c) 243 (d) 244
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 75? (a) 5 (b) 8 (c) 7 (d) 6
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 16 (b) 6 (c) 18 (d) 17
  19. 19.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
  20. 20.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) 39 (b) 36 (c) 108 (d) 12
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 9 (b) 10 (c) 8 (d) 7
  22. 22.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) 18 (d) 45
  23. 23.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 9 (d) 10
  24. 24.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 267 (c) 277 (d) 256
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 16 (b) 4 (c) 14 (d) 15
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 1 (b) 4 (c) 2 (d) 3
  27. 27.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 13 (d) 8
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 17 (b) 18 (c) 19 (d) 7
  29. 29.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 169 (c) 160 (d) 170
  30. 30.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
  31. 31.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 242 (b) 246 (c) 255 (d) 256
  32. 32.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 149 (c) 158 (d) 150
  33. 33.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 420 (c) 421 (d) 352
  34. 34.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 17 (b) 15 (c) 6 (d) 16
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 31? (a) 3 (b) 4 (c) 1 (d) 2
  37. 37.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  38. 38.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) 63 (b) 189 (c) 21 (d) 66
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 64? (a) 6 (b) 7 (c) 4 (d) 5
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 66? (a) 15 (b) 6 (c) 14 (d) 13

Answer key

  1. 15
  2. 66
  3. 18
  4. 2
  5. 27
  6. 3
  7. 13
  8. 51
  9. 43
  10. 6
  11. 18
  12. 7
  13. 189
  14. 41
  15. 30
  16. 243
  17. 7
  18. 17
  19. 72
  20. 36
  21. 9
  22. 15
  23. 8
  24. 276
  25. 15
  26. 3
  27. 7
  28. 18
  29. 169
  30. 9
  31. 255
  32. 149
  33. 420
  34. 3
  35. 16
  36. 3
  37. 5
  38. 63
  39. 6
  40. 14

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