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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 95 · 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 2? (a) 10 (b) 1 (c) 3 (d) 2
  2. 2.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  3. 3.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  4. 4.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 540 (b) 550 (c) 549 (d) 438
  5. 5.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 45 (c) 36 (d) 54
  6. 6.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 356 (c) 427 (d) 426
  7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 15 (b) 17 (c) 5 (d) 16
  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 8? (a) 8 (b) 10 (c) 7 (d) 9
  10. 10.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) 15 (b) 18 (c) 5 (d) 45
  11. 11.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) 39 (c) 42 (d) 117
  12. 12.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 104 (c) 103 (d) 112
  13. 13.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 9 (b) 18 (c) 19 (d) 20
  15. 15.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) 57 (b) 18 (c) 54 (d) 162
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 5 (b) 6 (c) 7 (d) 8
  17. 17.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) 69 (c) 207 (d) 23
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 7 (b) 6 (c) 5 (d) 4
  19. 19.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) 171 (c) 57 (d) 19
  20. 20.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 80 (c) 89 (d) 90
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 20 (b) 19 (c) 9 (d) 18
  22. 22.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 15 (b) 16 (c) 5 (d) 17
  24. 24.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  25. 25.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 40 (c) 58 (d) 49
  26. 26.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 249 (c) 258 (d) 259
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 2 (b) 5 (c) 3 (d) 4
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 20 (b) 19 (c) 8 (d) 18
  29. 29.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 42 (c) 51 (d) 52
  30. 30.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 386 (b) 471 (c) 472 (d) 462
  31. 31.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) 9 (d) 81
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 19 (b) 7 (c) 18 (d) 17
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 4 (b) 2 (c) 3 (d) 1
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 17 (b) 19 (c) 7 (d) 18
  35. 35.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  36. 36.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
  37. 37.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5
  38. 38.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 13 (d) 8
  39. 39.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 325 (b) 288 (c) 315 (d) 324
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 8 (d) 19

Answer key

  1. 2
  2. 3
  3. 7
  4. 549
  5. 45
  6. 426
  7. 16
  8. 30
  9. 8
  10. 15
  11. 39
  12. 103
  13. 5
  14. 19
  15. 54
  16. 7
  17. 69
  18. 6
  19. 57
  20. 89
  21. 19
  22. 6
  23. 16
  24. 6
  25. 49
  26. 258
  27. 4
  28. 19
  29. 51
  30. 471
  31. 27
  32. 18
  33. 3
  34. 18
  35. 9
  36. 61
  37. 4
  38. 7
  39. 324
  40. 19

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