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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 894 · 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 times is the digit 5 written when you write all the numbers from 1 to 96? (a) 21 (b) 19 (c) 9 (d) 20
  2. 2.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) 253 (c) 243 (d) 252
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 46? (a) 13 (b) 12 (c) 11 (d) 4
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 14 (b) 3 (c) 15 (d) 13
  5. 5.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  6. 6.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) 472 (c) 591 (d) 601
  7. 7.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 16 (b) 6 (c) 18 (d) 17
  9. 9.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  10. 10.The numbers 15 to 23 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) 60 (c) 171 (d) 19
  11. 11.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 89 (c) 90 (d) 98
  12. 12.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 570 (c) 452 (d) 571
  13. 13.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) 14 (c) 42 (d) 126
  14. 14.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) 54 (b) 6 (c) 21 (d) 18
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 58? (a) 17 (b) 5 (c) 16 (d) 15
  16. 16.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) 24 (c) 21 (d) 7
  17. 17.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 91 (c) 92 (d) 82
  18. 18.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 280 (c) 258 (d) 279
  19. 19.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) 33 (b) 30 (c) 90 (d) 10
  20. 20.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 240 (c) 249 (d) 238
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 3 (b) 5 (c) 4 (d) 2
  22. 22.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) 66 (b) 63 (c) 21 (d) 189
  23. 23.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 380 (b) 463 (c) 462 (d) 453
  24. 24.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) 15 (b) 135 (c) 45 (d) 48
  25. 25.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 470 (b) 598 (c) 597 (d) 588
  26. 26.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 127 (c) 128 (d) 136
  27. 27.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 376 (c) 457 (d) 456
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 6 (b) 5 (c) 4 (d) 3
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 13 (b) 3 (c) 15 (d) 14
  30. 30.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 90? (a) 19 (b) 20 (c) 9 (d) 18
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 4 (b) 14 (c) 16 (d) 15
  33. 33.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 445 (b) 435 (c) 368 (d) 444
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 99? (a) 21 (b) 19 (c) 9 (d) 20
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 19 (b) 9 (c) 20 (d) 21
  36. 36.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) 27 (b) 81 (c) 30 (d) 9
  37. 37.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 2 (b) 3 (c) 4 (d) 5
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 14 (b) 16 (c) 4 (d) 15
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 64? (a) 7 (b) 5 (c) 4 (d) 6

Answer key

  1. 20
  2. 252
  3. 12
  4. 14
  5. 3
  6. 600
  7. 8
  8. 17
  9. 4
  10. 57
  11. 89
  12. 570
  13. 42
  14. 18
  15. 16
  16. 21
  17. 91
  18. 279
  19. 30
  20. 249
  21. 4
  22. 63
  23. 462
  24. 45
  25. 597
  26. 127
  27. 456
  28. 5
  29. 14
  30. 9
  31. 19
  32. 15
  33. 444
  34. 20
  35. 20
  36. 27
  37. 5
  38. 4
  39. 15
  40. 6

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