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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 7 · 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 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 97 (c) 88 (d) 106
  2. 2.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 1 (d) 18
  3. 3.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) 117 (b) 13 (c) 42 (d) 39
  4. 4.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) 81 (b) 9 (c) 30 (d) 27
  5. 5.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 18 (b) 20 (c) 19 (d) 9
  7. 7.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) 51 (b) 48 (c) 144 (d) 16
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 4 (b) 6 (c) 5 (d) 3
  9. 9.The numbers 11 to 19 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) 48 (d) 135
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 14 (b) 15 (c) 16 (d) 4
  11. 11.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 80 (c) 62 (d) 71
  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) 72 (b) 27 (c) 24 (d) 8
  13. 13.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 181 (b) 182 (c) 190 (d) 172
  14. 14.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) 12 (b) 108 (c) 36 (d) 39
  15. 15.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  16. 16.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) 6 (b) 21 (c) 18 (d) 54
  17. 17.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 3 (b) 5 (c) 6 (d) 4
  18. 18.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 5 (d) 10
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 14 (b) 13 (c) 15 (d) 3
  20. 20.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 78 (c) 70 (d) 69
  21. 21.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 492 (c) 631 (d) 630
  22. 22.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) 60 (b) 20 (c) 180 (d) 63
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 8 (b) 5 (c) 6 (d) 7
  24. 24.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 463 (b) 453 (c) 380 (d) 462
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 6 (b) 5 (c) 4 (d) 3
  26. 26.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) 5 (c) 18 (d) 15
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 2 (b) 4 (c) 3 (d) 5
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 12 (b) 5 (c) 11 (d) 13
  29. 29.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 161 (c) 162 (d) 170
  30. 30.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 288 (c) 315 (d) 325
  31. 31.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) 23 (d) 69
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 21 (b) 20 (c) 19 (d) 9
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 7 (b) 6 (c) 5 (d) 8
  34. 34.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 414 (c) 514 (d) 504
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 19 (b) 18 (c) 20 (d) 8
  36. 36.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) 51 (c) 17 (d) 54
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 18 (b) 6 (c) 17 (d) 16
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 97? (a) 21 (b) 20 (c) 9 (d) 19
  39. 39.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 226 (c) 231 (d) 232
  40. 40.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) 22 (b) 69 (c) 66 (d) 198

Answer key

  1. 97
  2. 2
  3. 39
  4. 27
  5. 7
  6. 19
  7. 48
  8. 5
  9. 45
  10. 15
  11. 71
  12. 24
  13. 181
  14. 36
  15. 5
  16. 18
  17. 5
  18. 4
  19. 14
  20. 69
  21. 630
  22. 60
  23. 7
  24. 462
  25. 5
  26. 15
  27. 4
  28. 12
  29. 161
  30. 324
  31. 69
  32. 20
  33. 7
  34. 513
  35. 19
  36. 51
  37. 17
  38. 20
  39. 231
  40. 66

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