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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 43 · 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 10? (a) 11 (b) 9 (c) 8 (d) 10
  2. 2.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 21 (b) 19 (c) 9 (d) 20
  4. 4.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) 198 (b) 22 (c) 66 (d) 69
  5. 5.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 6 (b) 8 (c) 7 (d) 9
  7. 7.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 45 (c) 36 (d) 54
  8. 8.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
  9. 9.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 304 (c) 348 (d) 349
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 3 (b) 6 (c) 4 (d) 5
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 99? (a) 9 (b) 20 (c) 21 (d) 19
  12. 12.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) 153 (b) 54 (c) 17 (d) 51
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 58? (a) 5 (b) 3 (c) 6 (d) 4
  14. 14.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 538 (c) 528 (d) 537
  15. 15.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  16. 16.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 159 (b) 160 (c) 150 (d) 168
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 66? (a) 16 (b) 6 (c) 18 (d) 17
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 99? (a) 21 (b) 20 (c) 19 (d) 9
  19. 19.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 48 (c) 57 (d) 66
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 85? (a) 18 (b) 20 (c) 19 (d) 8
  21. 21.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) 90 (d) 30
  22. 22.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) 81 (b) 9 (c) 27 (d) 30
  23. 23.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 225 (c) 235 (d) 234
  24. 24.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) 23 (b) 207 (c) 72 (d) 69
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 2 (b) 3 (c) 1 (d) 4
  26. 26.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 386 (b) 471 (c) 472 (d) 462
  27. 27.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  28. 28.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 337 (c) 327 (d) 296
  29. 29.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 7 (d) 8
  30. 30.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 378 (c) 379 (d) 369
  31. 31.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  32. 32.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) 24 (c) 63 (d) 21
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 67? (a) 14 (b) 16 (c) 15 (d) 6
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 17 (b) 18 (c) 19 (d) 8
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 5 (b) 4 (c) 3 (d) 2
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 74? (a) 6 (b) 7 (c) 8 (d) 5
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 16 (b) 17 (c) 18 (d) 7
  38. 38.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) 63 (b) 60 (c) 20 (d) 180
  39. 39.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 444 (c) 445 (d) 368
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 18 (b) 17 (c) 6 (d) 16

Answer key

  1. 9
  2. 3
  3. 20
  4. 66
  5. 4
  6. 8
  7. 45
  8. 72
  9. 348
  10. 5
  11. 20
  12. 51
  13. 5
  14. 537
  15. 4
  16. 159
  17. 17
  18. 20
  19. 57
  20. 19
  21. 30
  22. 27
  23. 234
  24. 69
  25. 3
  26. 471
  27. 6
  28. 336
  29. 7
  30. 378
  31. 8
  32. 21
  33. 15
  34. 18
  35. 4
  36. 7
  37. 17
  38. 60
  39. 444
  40. 17

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