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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 555 · 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 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 386 (b) 472 (c) 462 (d) 471
  2. 2.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 250 (c) 238 (d) 240
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 8 (b) 18 (c) 19 (d) 20
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 9 (b) 20 (c) 19 (d) 21
  5. 5.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  6. 6.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
  7. 7.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  8. 8.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) 180 (b) 63 (c) 20 (d) 60
  9. 9.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) 48 (b) 15 (c) 45 (d) 135
  10. 10.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 4 (b) 1 (c) 3 (d) 2
  12. 12.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  13. 13.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 355 (c) 354 (d) 308
  14. 14.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  15. 15.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) 180 (c) 198 (d) 189
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 15 (b) 16 (c) 5 (d) 14
  17. 17.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) 63 (b) 21 (c) 24 (d) 7
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 4 (b) 5 (c) 7 (d) 6
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 7 (b) 4 (c) 6 (d) 5
  20. 20.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 7 (d) 6
  21. 21.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  22. 22.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 98? (a) 9 (b) 21 (c) 19 (d) 20
  24. 24.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 7 (b) 4 (c) 6 (d) 5
  26. 26.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
  27. 27.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 325 (c) 288 (d) 324
  28. 28.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 16 (b) 18 (c) 9 (d) 19
  30. 30.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 56? (a) 6 (b) 5 (c) 4 (d) 3
  32. 32.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 344 (c) 399 (d) 409
  33. 33.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) 51 (b) 54 (c) 17 (d) 153
  34. 34.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) 207 (c) 69 (d) 23
  35. 35.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 47 (c) 48 (d) 56
  36. 36.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 9 (d) 12
  37. 37.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 6 (d) 14
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 15 (b) 18 (c) 9 (d) 17
  39. 39.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) 45 (b) 5 (c) 18 (d) 15
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 3 (b) 1 (c) 4 (d) 2

Answer key

  1. 471
  2. 249
  3. 19
  4. 20
  5. 2
  6. 66
  7. 3
  8. 60
  9. 45
  10. 5
  11. 3
  12. 8
  13. 354
  14. 9
  15. 189
  16. 15
  17. 21
  18. 6
  19. 6
  20. 7
  21. 4
  22. 5
  23. 20
  24. 9
  25. 6
  26. 27
  27. 324
  28. 6
  29. 18
  30. 2
  31. 5
  32. 408
  33. 51
  34. 69
  35. 47
  36. 8
  37. 6
  38. 17
  39. 15
  40. 3

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