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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 281 · 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 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) 18 (d) 54
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 9 (b) 20 (c) 19 (d) 21
  3. 3.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 4 (d) 17
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 59? (a) 17 (b) 16 (c) 5 (d) 15
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 5 (b) 2 (c) 4 (d) 3
  6. 6.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 1 (b) 3 (c) 2 (d) 4
  8. 8.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
  9. 9.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  10. 10.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 247 (b) 246 (c) 236 (d) 237
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 18 (b) 7 (c) 17 (d) 19
  12. 12.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 56? (a) 6 (b) 4 (c) 5 (d) 3
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 4 (b) 5 (c) 3 (d) 2
  15. 15.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  16. 16.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  17. 17.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
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 3 (d) 1
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 15 (b) 16 (c) 14 (d) 4
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 66? (a) 18 (b) 16 (c) 6 (d) 17
  21. 21.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 15 (b) 4 (c) 14 (d) 16
  23. 23.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) 13 (b) 42 (c) 117 (d) 39
  24. 24.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) 171 (d) 19
  25. 25.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) 12 (c) 36 (d) 108
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 20 (b) 18 (c) 8 (d) 19
  27. 27.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 19 (b) 20 (c) 21 (d) 9
  29. 29.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 379 (b) 324 (c) 369 (d) 378
  30. 30.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 24 (b) 42 (c) 34 (d) 33
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 17 (b) 18 (c) 19 (d) 7
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 5 (b) 3 (c) 4 (d) 2
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 2 (b) 3 (c) 5 (d) 4
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 6 (b) 11 (c) 12 (d) 9
  35. 35.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) 16 (b) 48 (c) 144 (d) 51
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 5 (b) 3 (c) 4 (d) 6
  37. 37.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 121 (b) 112 (c) 122 (d) 130
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 58? (a) 15 (b) 5 (c) 16 (d) 17
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 3 (b) 4 (c) 5 (d) 2
  40. 40.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 7 (d) 9

Answer key

  1. 54
  2. 20
  3. 3
  4. 16
  5. 4
  6. 9
  7. 3
  8. 30
  9. 5
  10. 246
  11. 18
  12. 6
  13. 5
  14. 4
  15. 4
  16. 3
  17. 60
  18. 3
  19. 15
  20. 17
  21. 6
  22. 15
  23. 39
  24. 57
  25. 36
  26. 19
  27. 9
  28. 20
  29. 378
  30. 33
  31. 18
  32. 4
  33. 4
  34. 11
  35. 48
  36. 5
  37. 121
  38. 16
  39. 4
  40. 8

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