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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 388 · 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 12? (a) 8 (b) 13 (c) 7 (d) 6
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 73? (a) 17 (b) 18 (c) 7 (d) 16
  3. 3.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 164 (c) 155 (d) 156
  4. 4.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 7 (d) 9
  5. 5.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 144 (b) 16 (c) 51 (d) 48
  6. 6.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  7. 7.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 453 (b) 463 (c) 380 (d) 462
  8. 8.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 140 (c) 150 (d) 149
  9. 9.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  10. 10.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 5 (d) 3
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 70? (a) 7 (b) 18 (c) 17 (d) 16
  12. 12.The numbers 17 to 25 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) 63 (c) 189 (d) 66
  13. 13.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) 9 (b) 27 (c) 81 (d) 30
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 75? (a) 16 (b) 7 (c) 17 (d) 18
  15. 15.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 164 (c) 154 (d) 163
  16. 16.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 416 (b) 516 (c) 507 (d) 517
  17. 17.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 246 (c) 255 (d) 242
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 20 (b) 19 (c) 9 (d) 18
  19. 19.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) 51 (c) 17 (d) 54
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 16 (b) 4 (c) 15 (d) 14
  21. 21.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 11 (d) 8
  22. 22.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  23. 23.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 11 (d) 10
  24. 24.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 631 (b) 630 (c) 492 (d) 621
  25. 25.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) 18 (b) 21 (c) 54 (d) 6
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 7 (b) 17 (c) 16 (d) 18
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 38? (a) 3 (b) 2 (c) 4 (d) 5
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 97? (a) 21 (b) 20 (c) 9 (d) 19
  29. 29.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) 45 (c) 18 (d) 5
  30. 30.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 404 (c) 498 (d) 499
  31. 31.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 19 (b) 20 (c) 9 (d) 21
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 19 (b) 9 (c) 18 (d) 20
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 2 (b) 4 (c) 3 (d) 1
  35. 35.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 362 (c) 436 (d) 426
  36. 36.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 194 (b) 176 (c) 186 (d) 185
  37. 37.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  38. 38.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 507 (c) 508 (d) 410
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 3 (d) 5
  40. 40.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 17 (d) 3

Answer key

  1. 7
  2. 17
  3. 155
  4. 8
  5. 48
  6. 3
  7. 462
  8. 149
  9. 2
  10. 4
  11. 17
  12. 63
  13. 27
  14. 17
  15. 163
  16. 516
  17. 255
  18. 19
  19. 51
  20. 15
  21. 9
  22. 5
  23. 9
  24. 630
  25. 18
  26. 17
  27. 4
  28. 20
  29. 15
  30. 498
  31. 2
  32. 20
  33. 19
  34. 3
  35. 435
  36. 185
  37. 4
  38. 507
  39. 4
  40. 3

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