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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 450 · 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 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) 81 (c) 27 (d) 9
  2. 2.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 73? (a) 16 (b) 7 (c) 17 (d) 18
  4. 4.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 386 (c) 462 (d) 471
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 85? (a) 18 (b) 20 (c) 8 (d) 19
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 4 (b) 1 (c) 3 (d) 2
  7. 7.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 540 (c) 541 (d) 432
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 15 (b) 5 (c) 14 (d) 16
  9. 9.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) 21 (b) 63 (c) 24 (d) 7
  10. 10.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  11. 11.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 294 (c) 333 (d) 334
  12. 12.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) 8 (b) 72 (c) 24 (d) 27
  13. 13.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 66? (a) 6 (b) 14 (c) 13 (d) 15
  15. 15.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) 18 (b) 54 (c) 6 (d) 21
  16. 16.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 18 (b) 19 (c) 7 (d) 17
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 20 (b) 9 (c) 19 (d) 21
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 4 (b) 2 (c) 3 (d) 5
  20. 20.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  21. 21.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 20 (c) 60 (d) 63
  22. 22.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) 39 (b) 108 (c) 36 (d) 12
  23. 23.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 361 (b) 360 (c) 312 (d) 351
  24. 24.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 2 (b) 3 (c) 5 (d) 4
  26. 26.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 391 (c) 332 (d) 381
  27. 27.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  28. 28.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 625 (c) 624 (d) 488
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 17 (b) 15 (c) 5 (d) 16
  30. 30.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 78 (c) 60 (d) 69
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 19 (b) 9 (c) 21 (d) 20
  32. 32.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 34 (c) 43 (d) 52
  33. 33.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) 24 (b) 72 (c) 216 (d) 75
  34. 34.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) 42 (b) 126 (c) 14 (d) 45
  35. 35.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 162 (b) 57 (c) 54 (d) 18
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 18 (b) 6 (c) 17 (d) 16
  37. 37.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  38. 38.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 39 (c) 30 (d) 48
  39. 39.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 340 (b) 403 (c) 393 (d) 402
  40. 40.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) 189 (b) 66 (c) 21 (d) 63

Answer key

  1. 27
  2. 4
  3. 17
  4. 471
  5. 19
  6. 3
  7. 540
  8. 15
  9. 21
  10. 2
  11. 333
  12. 24
  13. 3
  14. 14
  15. 18
  16. 5
  17. 18
  18. 20
  19. 4
  20. 6
  21. 60
  22. 36
  23. 360
  24. 3
  25. 4
  26. 390
  27. 4
  28. 624
  29. 16
  30. 69
  31. 20
  32. 43
  33. 72
  34. 42
  35. 54
  36. 17
  37. 5
  38. 39
  39. 402
  40. 63

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