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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 420 · 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 9? (a) 9 (b) 11 (c) 8 (d) 10
  2. 2.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  3. 3.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) 72 (b) 8 (c) 27 (d) 24
  4. 4.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 310 (c) 278 (d) 309
  5. 5.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) 296 (c) 327 (d) 337
  6. 6.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 66 (c) 56 (d) 65
  7. 7.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 420 (c) 429 (d) 358
  8. 8.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 510 (c) 520 (d) 519
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 6 (b) 4 (c) 5 (d) 3
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 6 (b) 7 (c) 4 (d) 3
  11. 11.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 466 (c) 582 (d) 592
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 7 (b) 6 (c) 5 (d) 8
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 2 (b) 3 (c) 4 (d) 5
  14. 14.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 3 (d) 1
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 20 (b) 19 (c) 18 (d) 9
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 3 (b) 13 (c) 14 (d) 12
  17. 17.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 4 (b) 3 (c) 5 (d) 6
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 16 (b) 17 (c) 6 (d) 18
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 91? (a) 19 (b) 18 (c) 9 (d) 20
  21. 21.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 3 (b) 2 (c) 5 (d) 4
  23. 23.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) 18 (b) 54 (c) 162 (d) 57
  24. 24.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 2 (d) 4
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 40? (a) 4 (b) 5 (c) 3 (d) 6
  26. 26.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) 135 (b) 15 (c) 48 (d) 45
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 15 (b) 3 (c) 13 (d) 14
  28. 28.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11
  29. 29.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 80? (a) 7 (b) 9 (c) 6 (d) 8
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 4 (b) 2 (c) 1 (d) 3
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 64? (a) 16 (b) 17 (c) 15 (d) 6
  33. 33.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 324 (c) 379 (d) 369
  34. 34.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 210 (c) 198 (d) 208
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 1 (b) 2 (c) 3 (d) 4
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 15 (b) 14 (c) 16 (d) 4
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 62? (a) 4 (b) 5 (c) 7 (d) 6
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 8 (b) 5 (c) 6 (d) 7
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 4 (b) 5 (c) 6 (d) 3
  40. 40.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) 20 (b) 60 (c) 63 (d) 180

Answer key

  1. 9
  2. 7
  3. 24
  4. 309
  5. 336
  6. 65
  7. 429
  8. 519
  9. 5
  10. 6
  11. 591
  12. 7
  13. 4
  14. 2
  15. 19
  16. 13
  17. 6
  18. 5
  19. 17
  20. 19
  21. 7
  22. 4
  23. 54
  24. 3
  25. 5
  26. 45
  27. 14
  28. 9
  29. 4
  30. 8
  31. 3
  32. 16
  33. 378
  34. 207
  35. 3
  36. 15
  37. 6
  38. 7
  39. 5
  40. 60

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