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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 623 · 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 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 470 (b) 598 (c) 588 (d) 597
  2. 2.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 26 (c) 35 (d) 36
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 16 (b) 15 (c) 5 (d) 14
  4. 4.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  5. 5.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 450 (c) 558 (d) 568
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 54? (a) 15 (b) 17 (c) 5 (d) 16
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 18 (b) 6 (c) 16 (d) 17
  8. 8.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 532 (c) 531 (d) 426
  9. 9.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 225 (b) 226 (c) 216 (d) 222
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 2 (b) 5 (c) 4 (d) 3
  11. 11.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 130 (c) 129 (d) 120
  12. 12.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) 5 (b) 15 (c) 45 (d) 18
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 15 (b) 17 (c) 16 (d) 6
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 19 (b) 7 (c) 17 (d) 18
  15. 15.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) 36 (b) 33 (c) 99 (d) 11
  16. 16.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 12 (c) 108 (d) 39
  17. 17.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 322 (c) 312 (d) 321
  18. 18.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  19. 19.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) 66 (c) 189 (d) 63
  20. 20.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 375 (b) 328 (c) 385 (d) 384
  21. 21.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 198 (b) 69 (c) 66 (d) 22
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 69? (a) 16 (b) 17 (c) 6 (d) 18
  23. 23.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 231 (c) 241 (d) 232
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 2 (b) 3 (c) 4 (d) 5
  25. 25.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) 72 (b) 24 (c) 27 (d) 8
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 2 (b) 3 (c) 4 (d) 5
  27. 27.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) 30 (b) 27 (c) 81 (d) 9
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 2 (b) 4 (c) 1 (d) 3
  29. 29.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 355 (b) 354 (c) 308 (d) 345
  30. 30.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
  31. 31.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 75 (b) 216 (c) 72 (d) 24
  32. 32.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 616 (c) 482 (d) 615
  33. 33.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
  34. 34.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 80 (c) 71 (d) 72
  35. 35.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 72 (c) 69 (d) 23
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 43? (a) 4 (b) 5 (c) 2 (d) 3
  37. 37.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
  38. 38.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 198 (c) 189 (d) 180
  39. 39.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 504 (c) 495 (d) 505
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 21 (b) 19 (c) 20 (d) 9

Answer key

  1. 597
  2. 35
  3. 15
  4. 7
  5. 567
  6. 16
  7. 17
  8. 531
  9. 225
  10. 4
  11. 129
  12. 15
  13. 16
  14. 18
  15. 33
  16. 36
  17. 321
  18. 2
  19. 63
  20. 384
  21. 66
  22. 17
  23. 240
  24. 4
  25. 24
  26. 4
  27. 27
  28. 3
  29. 354
  30. 8
  31. 72
  32. 615
  33. 4
  34. 71
  35. 69
  36. 4
  37. 3
  38. 189
  39. 504
  40. 20

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