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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 785 · 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 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 420 (c) 513 (d) 523
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 49? (a) 4 (b) 5 (c) 6 (d) 3
  3. 3.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 384 (c) 334 (d) 394
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 1 (b) 3 (c) 4 (d) 2
  5. 5.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  6. 6.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 381 (c) 326 (d) 372
  7. 7.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 7 (d) 5
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 16 (b) 14 (c) 5 (d) 15
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 16 (b) 15 (c) 4 (d) 14
  10. 10.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 9 (d) 7
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 19 (d) 18
  12. 12.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 490 (c) 480 (d) 398
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 13 (b) 15 (c) 3 (d) 14
  14. 14.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) 57 (b) 18 (c) 162 (d) 54
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 17 (b) 19 (c) 7 (d) 18
  16. 16.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 304 (c) 303 (d) 274
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 4 (d) 5
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 15 (b) 5 (c) 16 (d) 17
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 3 (b) 4 (c) 2 (d) 5
  20. 20.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 252 (c) 243 (d) 253
  21. 21.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  22. 22.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  23. 23.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 14 (b) 5 (c) 15 (d) 16
  25. 25.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 510 (c) 520 (d) 519
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 3 (b) 4 (c) 2 (d) 5
  27. 27.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
  28. 28.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 70 (c) 52 (d) 61
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 10 (b) 12 (c) 11 (d) 3
  30. 30.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) 54 (c) 18 (d) 6
  31. 31.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 117 (c) 42 (d) 39
  32. 32.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  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) 17 (c) 54 (d) 153
  34. 34.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 9 (d) 7
  35. 35.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) 33 (b) 99 (c) 36 (d) 11
  36. 36.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 313 (c) 303 (d) 312
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 37? (a) 2 (b) 1 (c) 3 (d) 4
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 56? (a) 7 (b) 5 (c) 6 (d) 4
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 44? (a) 5 (b) 4 (c) 2 (d) 3
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 9 (b) 18 (c) 20 (d) 19

Answer key

  1. 522
  2. 5
  3. 393
  4. 3
  5. 9
  6. 381
  7. 6
  8. 15
  9. 15
  10. 8
  11. 19
  12. 489
  13. 14
  14. 54
  15. 18
  16. 303
  17. 4
  18. 16
  19. 4
  20. 252
  21. 7
  22. 3
  23. 3
  24. 15
  25. 519
  26. 4
  27. 2
  28. 61
  29. 11
  30. 18
  31. 39
  32. 5
  33. 51
  34. 8
  35. 33
  36. 312
  37. 3
  38. 6
  39. 4
  40. 19

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