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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 362 · 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 5? (a) 6 (b) 10 (c) 4 (d) 5
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 13 (b) 11 (c) 5 (d) 12
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 91? (a) 18 (b) 20 (c) 9 (d) 19
  4. 4.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 7 (b) 18 (c) 19 (d) 17
  6. 6.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 550 (b) 540 (c) 438 (d) 549
  7. 7.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) 45 (c) 126 (d) 14
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 20 (d) 9
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 17 (b) 16 (c) 6 (d) 18
  10. 10.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 18 (b) 17 (c) 19 (d) 8
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 54? (a) 15 (b) 16 (c) 5 (d) 17
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 19 (b) 9 (c) 20 (d) 21
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 9 (b) 10 (c) 11 (d) 4
  16. 16.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 436 (c) 426 (d) 362
  17. 17.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) 54 (c) 18 (d) 57
  18. 18.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 219 (c) 224 (d) 229
  19. 19.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 541 (b) 531 (c) 540 (d) 432
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 3 (b) 13 (c) 14 (d) 15
  21. 21.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 90 (c) 72 (d) 81
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 2 (b) 1 (c) 4 (d) 3
  23. 23.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
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 64? (a) 4 (b) 5 (c) 6 (d) 7
  25. 25.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 374 (b) 454 (c) 444 (d) 453
  26. 26.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 4 (d) 17
  27. 27.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) 63 (c) 66 (d) 21
  28. 28.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) 39 (c) 13 (d) 42
  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) 52 (d) 51
  30. 30.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 6 (d) 4
  31. 31.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 17 (b) 15 (c) 16 (d) 5
  33. 33.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  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) 15 (b) 45 (c) 135 (d) 48
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 20 (b) 9 (c) 18 (d) 19
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 13 (b) 15 (c) 14 (d) 3
  37. 37.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) 36 (c) 108 (d) 12
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 3 (b) 4 (c) 5 (d) 6
  39. 39.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  40. 40.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 11 (c) 33 (d) 36

Answer key

  1. 5
  2. 12
  3. 19
  4. 6
  5. 18
  6. 549
  7. 42
  8. 20
  9. 17
  10. 4
  11. 18
  12. 9
  13. 16
  14. 20
  15. 10
  16. 435
  17. 54
  18. 228
  19. 540
  20. 14
  21. 81
  22. 3
  23. 60
  24. 6
  25. 453
  26. 3
  27. 63
  28. 39
  29. 51
  30. 5
  31. 8
  32. 16
  33. 9
  34. 45
  35. 19
  36. 14
  37. 36
  38. 5
  39. 7
  40. 33

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