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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 948 · 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.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) 30 (c) 33 (d) 10
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 65? (a) 17 (b) 6 (c) 16 (d) 18
  3. 3.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  4. 4.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 89 (b) 98 (c) 90 (d) 80
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 2 (b) 3 (c) 1 (d) 4
  6. 6.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) 45 (b) 15 (c) 18 (d) 5
  7. 7.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 88? (a) 18 (b) 8 (c) 20 (d) 19
  9. 9.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  10. 10.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) 24 (b) 27 (c) 8 (d) 72
  11. 11.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
  12. 12.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 472 (c) 386 (d) 471
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 88? (a) 20 (b) 18 (c) 8 (d) 19
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 12 (b) 13 (c) 11 (d) 5
  15. 15.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) 126 (c) 42 (d) 14
  16. 16.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 14 (d) 15
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 13 (b) 14 (c) 3 (d) 15
  19. 19.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) 66 (c) 69 (d) 22
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 6 (b) 17 (c) 18 (d) 16
  21. 21.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) 6 (d) 18
  22. 22.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 316 (c) 357 (d) 367
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 1 (d) 3
  24. 24.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) 7 (d) 21
  25. 25.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  26. 26.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 178 (c) 187 (d) 188
  27. 27.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  28. 28.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 171 (b) 162 (c) 180 (d) 172
  29. 29.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 84 (c) 83 (d) 74
  30. 30.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 522 (c) 523 (d) 420
  31. 31.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) 144 (b) 51 (c) 16 (d) 48
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 10 (b) 11 (c) 5 (d) 8
  33. 33.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 5 (d) 3
  34. 34.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) 372 (c) 326 (d) 381
  35. 35.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 5 (d) 7
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 33? (a) 3 (b) 7 (c) 9 (d) 8
  37. 37.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 322 (c) 321 (d) 286
  38. 38.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 519 (b) 528 (c) 424 (d) 529
  39. 39.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 34 (c) 33 (d) 24
  40. 40.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) 17 (b) 54 (c) 153 (d) 51

Answer key

  1. 30
  2. 17
  3. 9
  4. 89
  5. 3
  6. 15
  7. 5
  8. 19
  9. 7
  10. 24
  11. 2
  12. 471
  13. 19
  14. 12
  15. 42
  16. 3
  17. 15
  18. 14
  19. 66
  20. 17
  21. 18
  22. 366
  23. 3
  24. 21
  25. 9
  26. 187
  27. 2
  28. 171
  29. 83
  30. 522
  31. 48
  32. 10
  33. 4
  34. 381
  35. 6
  36. 8
  37. 321
  38. 528
  39. 33
  40. 51

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