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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 167 · 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) 11 (b) 10 (c) 8 (d) 9
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 5 (b) 8 (c) 7 (d) 6
  3. 3.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 33 (c) 10 (d) 30
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 74? (a) 16 (b) 18 (c) 7 (d) 17
  5. 5.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  6. 6.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 39 (b) 48 (c) 30 (d) 40
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 5 (b) 15 (c) 16 (d) 17
  8. 8.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  9. 9.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 500 (b) 633 (c) 643 (d) 642
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 66? (a) 5 (b) 7 (c) 4 (d) 6
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 17 (b) 7 (c) 19 (d) 18
  12. 12.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  13. 13.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) 163 (d) 154
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 21 (b) 20 (c) 19 (d) 9
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 72? (a) 11 (b) 8 (c) 7 (d) 10
  16. 16.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 331 (c) 330 (d) 321
  17. 17.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
  18. 18.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  19. 19.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) 16 (b) 48 (c) 144 (d) 51
  20. 20.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 501 (b) 412 (c) 510 (d) 511
  21. 21.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 434 (c) 534 (d) 544
  22. 22.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) 42 (b) 45 (c) 126 (d) 14
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 16 (b) 18 (c) 6 (d) 17
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 20 (b) 8 (c) 18 (d) 19
  25. 25.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 421 (c) 411 (d) 420
  26. 26.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) 54 (d) 17
  27. 27.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 82? (a) 17 (b) 19 (c) 8 (d) 18
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 6 (b) 5 (c) 7 (d) 8
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 12 (b) 14 (c) 3 (d) 13
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 91? (a) 9 (b) 10 (c) 12 (d) 11
  32. 32.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 243 (c) 240 (d) 253
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 13 (b) 3 (c) 15 (d) 14
  34. 34.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) 63 (b) 189 (c) 21 (d) 66
  35. 35.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 450 (c) 460 (d) 459
  36. 36.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  37. 37.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 28 (c) 38 (d) 37
  38. 38.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 78 (c) 70 (d) 69
  39. 39.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 492 (c) 400 (d) 493
  40. 40.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 265 (c) 264 (d) 248

Answer key

  1. 9
  2. 7
  3. 30
  4. 17
  5. 2
  6. 39
  7. 16
  8. 7
  9. 642
  10. 6
  11. 18
  12. 6
  13. 163
  14. 20
  15. 10
  16. 330
  17. 18
  18. 3
  19. 48
  20. 510
  21. 543
  22. 42
  23. 17
  24. 19
  25. 420
  26. 51
  27. 4
  28. 18
  29. 7
  30. 13
  31. 11
  32. 252
  33. 14
  34. 63
  35. 459
  36. 9
  37. 37
  38. 69
  39. 492
  40. 264

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