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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 678 · 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 1 written when you write all the numbers from 1 to 94? (a) 9 (b) 21 (c) 20 (d) 19
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 19 (b) 21 (c) 9 (d) 20
  3. 3.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) 27 (b) 72 (c) 8 (d) 24
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 3 (b) 5 (c) 2 (d) 4
  5. 5.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) 72 (b) 69 (c) 207 (d) 23
  6. 6.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
  7. 7.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) 22 (c) 66 (d) 69
  8. 8.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 44 (c) 43 (d) 52
  9. 9.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  11. 11.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 151 (c) 142 (d) 160
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 17 (b) 19 (c) 7 (d) 18
  13. 13.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) 384 (c) 328 (d) 385
  14. 14.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 195 (c) 208 (d) 205
  15. 15.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 541 (b) 540 (c) 531 (d) 432
  16. 16.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) 60 (b) 57 (c) 19 (d) 171
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 21 (b) 19 (c) 9 (d) 20
  18. 18.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  19. 19.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 7 (d) 5
  20. 20.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 32? (a) 4 (b) 1 (c) 2 (d) 3
  22. 22.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) 54 (c) 51 (d) 17
  23. 23.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 15 (d) 4
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 45? (a) 2 (b) 5 (c) 3 (d) 4
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 6 (b) 5 (c) 3 (d) 4
  26. 26.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 142 (c) 150 (d) 141
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 18 (b) 20 (c) 19 (d) 8
  28. 28.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 46 (c) 64 (d) 55
  29. 29.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 517 (b) 416 (c) 516 (d) 507
  30. 30.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 456 (c) 382 (d) 466
  31. 31.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
  32. 32.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 19 (b) 20 (c) 8 (d) 18
  34. 34.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 453 (c) 454 (d) 374
  35. 35.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) 5 (c) 45 (d) 18
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 14 (b) 15 (c) 16 (d) 4
  37. 37.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) 99 (b) 11 (c) 33 (d) 36
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 20 (b) 18 (c) 19 (d) 8
  39. 39.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 123 (c) 114 (d) 124
  40. 40.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6

Answer key

  1. 20
  2. 20
  3. 24
  4. 4
  5. 69
  6. 7
  7. 66
  8. 43
  9. 5
  10. 7
  11. 151
  12. 18
  13. 384
  14. 204
  15. 540
  16. 57
  17. 20
  18. 4
  19. 6
  20. 2
  21. 3
  22. 51
  23. 5
  24. 4
  25. 5
  26. 141
  27. 19
  28. 55
  29. 516
  30. 465
  31. 3
  32. 8
  33. 19
  34. 453
  35. 15
  36. 15
  37. 33
  38. 19
  39. 123
  40. 6

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