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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 518 · 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 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 320 (c) 372 (d) 373
  2. 2.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 198 (c) 180 (d) 189
  3. 3.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  4. 4.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 5 (b) 2 (c) 4 (d) 3
  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) 30 (b) 90 (c) 33 (d) 10
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 14 (b) 3 (c) 15 (d) 13
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 65? (a) 4 (b) 6 (c) 7 (d) 5
  9. 9.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 559 (c) 549 (d) 444
  10. 10.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) 72 (b) 23 (c) 207 (d) 69
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 78? (a) 7 (b) 17 (c) 19 (d) 18
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 3 (b) 14 (c) 13 (d) 15
  13. 13.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) 8 (c) 27 (d) 72
  14. 14.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) 6 (c) 54 (d) 21
  15. 15.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) 22 (c) 66 (d) 198
  16. 16.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 17 (d) 3
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 49? (a) 5 (b) 3 (c) 4 (d) 6
  18. 18.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) 18 (c) 45 (d) 15
  19. 19.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) 21 (c) 63 (d) 189
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 7 (b) 5 (c) 6 (d) 4
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 19 (b) 17 (c) 8 (d) 18
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 7 (b) 6 (c) 8 (d) 5
  23. 23.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) 19 (c) 60 (d) 57
  24. 24.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 9 (d) 10
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 3 (b) 2 (c) 4 (d) 5
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 6 (b) 3 (c) 4 (d) 5
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 19 (b) 8 (c) 20 (d) 18
  28. 28.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 250 (c) 249 (d) 238
  29. 29.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
  30. 30.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  31. 31.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 4 (b) 7 (c) 5 (d) 6
  33. 33.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) 42 (c) 126 (d) 14
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 4 (b) 2 (c) 5 (d) 3
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 20 (b) 21 (c) 9 (d) 19
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 91? (a) 18 (b) 19 (c) 20 (d) 9
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 14 (b) 16 (c) 15 (d) 4
  38. 38.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 421 (b) 411 (c) 352 (d) 420
  39. 39.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 144 (c) 143 (d) 134
  40. 40.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 229 (b) 224 (c) 228 (d) 219

Answer key

  1. 372
  2. 189
  3. 6
  4. 4
  5. 4
  6. 30
  7. 14
  8. 6
  9. 558
  10. 69
  11. 18
  12. 14
  13. 24
  14. 18
  15. 66
  16. 3
  17. 5
  18. 15
  19. 63
  20. 6
  21. 18
  22. 7
  23. 57
  24. 8
  25. 4
  26. 5
  27. 19
  28. 249
  29. 5
  30. 2
  31. 8
  32. 6
  33. 42
  34. 4
  35. 20
  36. 19
  37. 15
  38. 420
  39. 143
  40. 228

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