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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 726 · 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.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  2. 2.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) 57 (b) 171 (c) 19 (d) 60
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 18 (b) 16 (c) 6 (d) 17
  4. 4.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 320 (b) 363 (c) 372 (d) 373
  5. 5.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) 9 (c) 30 (d) 81
  6. 6.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 253 (b) 243 (c) 240 (d) 252
  7. 7.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
  8. 8.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
  9. 9.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) 54 (c) 17 (d) 51
  10. 10.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) 21 (b) 66 (c) 63 (d) 189
  11. 11.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 16 (b) 18 (c) 17 (d) 7
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 3 (b) 4 (c) 6 (d) 5
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 6 (b) 16 (c) 15 (d) 17
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 1 (b) 2 (c) 4 (d) 3
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 17 (b) 7 (c) 19 (d) 18
  17. 17.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 171 (c) 180 (d) 172
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 8 (b) 18 (c) 19 (d) 20
  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) 69 (b) 198 (c) 66 (d) 22
  20. 20.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) 72 (b) 207 (c) 23 (d) 69
  21. 21.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 41 (b) 42 (c) 32 (d) 50
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 16 (b) 17 (c) 15 (d) 6
  24. 24.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
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 16 (b) 15 (c) 5 (d) 17
  26. 26.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 9 (d) 10
  27. 27.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 6 (b) 17 (c) 18 (d) 16
  29. 29.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 404 (c) 499 (d) 489
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 5 (b) 3 (c) 4 (d) 2
  31. 31.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 5 (b) 7 (c) 4 (d) 6
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 3 (b) 12 (c) 11 (d) 13
  34. 34.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) 135 (d) 48
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 38? (a) 2 (b) 3 (c) 4 (d) 5
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 15 (d) 14
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 17 (b) 19 (c) 8 (d) 18
  38. 38.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
  39. 39.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 501 (b) 412 (c) 511 (d) 510
  40. 40.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) 16 (c) 48 (d) 144

Answer key

  1. 3
  2. 57
  3. 17
  4. 372
  5. 27
  6. 252
  7. 9
  8. 3
  9. 51
  10. 63
  11. 6
  12. 17
  13. 5
  14. 16
  15. 3
  16. 18
  17. 171
  18. 19
  19. 66
  20. 69
  21. 41
  22. 2
  23. 16
  24. 60
  25. 16
  26. 8
  27. 9
  28. 17
  29. 498
  30. 4
  31. 5
  32. 6
  33. 12
  34. 45
  35. 4
  36. 15
  37. 18
  38. 30
  39. 510
  40. 48

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