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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 859 · 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 2? (a) 10 (b) 2 (c) 3 (d) 1
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 14 (b) 3 (c) 13 (d) 15
  3. 3.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) 207 (b) 69 (c) 72 (d) 23
  4. 4.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 628 (c) 618 (d) 627
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 2 (b) 4 (c) 5 (d) 3
  6. 6.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 423 (c) 354 (d) 414
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 56? (a) 3 (b) 6 (c) 4 (d) 5
  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) 21 (b) 6 (c) 18 (d) 54
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 16 (b) 7 (c) 17 (d) 18
  10. 10.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) 108 (b) 39 (c) 12 (d) 36
  11. 11.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) 180 (c) 60 (d) 20
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 6 (b) 7 (c) 8 (d) 5
  13. 13.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) 24 (b) 63 (c) 7 (d) 21
  14. 14.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  15. 15.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 18 (d) 1
  16. 16.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  17. 17.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 456 (c) 465 (d) 466
  18. 18.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 33 (c) 36 (d) 11
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 97? (a) 20 (b) 21 (c) 9 (d) 19
  20. 20.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 384 (c) 394 (d) 393
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 77? (a) 8 (b) 6 (c) 7 (d) 5
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 7 (b) 18 (c) 16 (d) 17
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 1 (b) 2 (c) 4 (d) 3
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 3 (b) 6 (c) 5 (d) 4
  25. 25.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 76 (c) 85 (d) 86
  26. 26.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 72 (c) 63 (d) 54
  27. 27.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 409 (c) 408 (d) 344
  28. 28.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 264 (c) 289 (d) 279
  29. 29.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 16 (b) 6 (c) 17 (d) 18
  31. 31.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 16 (b) 6 (c) 18 (d) 17
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 13 (b) 14 (c) 15 (d) 3
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 4 (b) 16 (c) 15 (d) 14
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 14 (b) 13 (c) 3 (d) 15
  36. 36.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 4 (b) 16 (c) 15 (d) 14
  38. 38.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) 45 (c) 18 (d) 15
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 5 (b) 4 (c) 3 (d) 2
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 4 (b) 2 (c) 3 (d) 5

Answer key

  1. 2
  2. 14
  3. 69
  4. 627
  5. 4
  6. 423
  7. 5
  8. 18
  9. 17
  10. 36
  11. 60
  12. 7
  13. 21
  14. 3
  15. 2
  16. 5
  17. 465
  18. 33
  19. 20
  20. 393
  21. 7
  22. 17
  23. 3
  24. 5
  25. 85
  26. 63
  27. 408
  28. 288
  29. 9
  30. 17
  31. 4
  32. 17
  33. 14
  34. 15
  35. 14
  36. 9
  37. 15
  38. 15
  39. 4
  40. 4

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