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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 302 · 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) 10 (b) 90 (c) 33 (d) 30
  2. 2.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 17 (b) 16 (c) 18 (d) 6
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 19 (b) 17 (c) 7 (d) 18
  5. 5.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  6. 6.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10
  7. 7.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) 30 (c) 81 (d) 9
  8. 8.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 13 (d) 6
  9. 9.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) 27 (c) 24 (d) 8
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 18 (b) 7 (c) 17 (d) 19
  11. 11.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  12. 12.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
  13. 13.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) 216 (b) 72 (c) 75 (d) 24
  14. 14.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) 42 (b) 117 (c) 13 (d) 39
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 18 (b) 19 (c) 8 (d) 17
  16. 16.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 189 (c) 204 (d) 199
  17. 17.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 5 (b) 6 (c) 3 (d) 4
  19. 19.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 404 (b) 489 (c) 499 (d) 498
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 9 (b) 3 (c) 10 (d) 8
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 16 (d) 15
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 16 (b) 15 (c) 5 (d) 14
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 7 (b) 19 (c) 18 (d) 17
  24. 24.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 313 (c) 312 (d) 280
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 5 (b) 17 (c) 15 (d) 16
  26. 26.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  27. 27.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) 7 (b) 63 (c) 21 (d) 24
  28. 28.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 360 (c) 312 (d) 361
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 14 (b) 13 (c) 15 (d) 3
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 93? (a) 20 (b) 9 (c) 18 (d) 19
  31. 31.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 402 (c) 340 (d) 403
  32. 32.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 137 (c) 128 (d) 138
  33. 33.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) 19 (b) 60 (c) 57 (d) 171
  34. 34.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) 52 (c) 70 (d) 61
  35. 35.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 2 (d) 3
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 4 (b) 14 (c) 16 (d) 15
  37. 37.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 282 (c) 292 (d) 266
  38. 38.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 7 (d) 9
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 52? (a) 4 (b) 3 (c) 5 (d) 6
  40. 40.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

Answer key

  1. 30
  2. 7
  3. 17
  4. 18
  5. 9
  6. 6
  7. 27
  8. 7
  9. 24
  10. 18
  11. 9
  12. 51
  13. 72
  14. 39
  15. 18
  16. 198
  17. 4
  18. 5
  19. 498
  20. 9
  21. 16
  22. 15
  23. 18
  24. 312
  25. 16
  26. 5
  27. 21
  28. 360
  29. 14
  30. 19
  31. 402
  32. 137
  33. 57
  34. 61
  35. 2
  36. 15
  37. 291
  38. 8
  39. 5
  40. 18

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