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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 359 · 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) 9 (b) 8 (c) 10 (d) 11
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 12 (b) 3 (c) 14 (d) 13
  3. 3.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 519 (b) 418 (c) 520 (d) 510
  4. 4.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) 8 (b) 72 (c) 27 (d) 24
  5. 5.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 476 (b) 597 (c) 606 (d) 607
  6. 6.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 36 (c) 46 (d) 45
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 18 (d) 1
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 4 (b) 13 (c) 14 (d) 15
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 3 (b) 4 (c) 2 (d) 5
  10. 10.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 55? (a) 17 (b) 5 (c) 16 (d) 15
  12. 12.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 586 (c) 585 (d) 462
  13. 13.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 175 (b) 166 (c) 176 (d) 184
  14. 14.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) 15 (b) 18 (c) 5 (d) 45
  15. 15.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 4 (b) 16 (c) 15 (d) 14
  17. 17.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
  18. 18.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 107 (b) 108 (c) 98 (d) 116
  19. 19.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
  20. 20.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 600 (b) 601 (c) 591 (d) 472
  21. 21.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 89 (b) 98 (c) 90 (d) 80
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 2 (b) 4 (c) 5 (d) 3
  23. 23.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 3 (b) 2 (c) 5 (d) 4
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 4 (b) 1 (c) 2 (d) 3
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 99? (a) 9 (b) 21 (c) 20 (d) 19
  27. 27.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) 54 (d) 18
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 58? (a) 17 (b) 5 (c) 15 (d) 16
  29. 29.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 51 (c) 60 (d) 42
  30. 30.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 405 (c) 415 (d) 414
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 5 (b) 3 (c) 2 (d) 4
  32. 32.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 15 (b) 16 (c) 5 (d) 17
  34. 34.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 6 (d) 10
  35. 35.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 619 (b) 609 (c) 618 (d) 484
  36. 36.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) 57 (d) 162
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 17 (b) 16 (c) 6 (d) 18
  38. 38.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 265 (c) 248 (d) 255
  39. 39.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 101 (b) 102 (c) 110 (d) 92
  40. 40.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 307 (c) 276 (d) 306

Answer key

  1. 9
  2. 13
  3. 519
  4. 24
  5. 606
  6. 45
  7. 2
  8. 14
  9. 4
  10. 4
  11. 16
  12. 585
  13. 175
  14. 15
  15. 3
  16. 15
  17. 42
  18. 107
  19. 5
  20. 600
  21. 89
  22. 4
  23. 8
  24. 4
  25. 3
  26. 20
  27. 18
  28. 16
  29. 51
  30. 414
  31. 4
  32. 4
  33. 16
  34. 5
  35. 618
  36. 54
  37. 17
  38. 264
  39. 101
  40. 306

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