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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 962 · 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 13? (a) 14 (b) 7 (c) 6 (d) 5
  2. 2.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 75 (b) 66 (c) 76 (d) 84
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 60? (a) 5 (b) 6 (c) 7 (d) 8
  4. 4.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) 8 (c) 24 (d) 27
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 7 (b) 8 (c) 6 (d) 5
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 19 (b) 20 (c) 18 (d) 8
  7. 7.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  8. 8.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) 54 (d) 18
  9. 9.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 15 (b) 13 (c) 3 (d) 14
  11. 11.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
  12. 12.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) 17 (b) 54 (c) 51 (d) 153
  13. 13.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 224 (c) 229 (d) 228
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 19 (b) 20 (c) 18 (d) 8
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 63? (a) 5 (b) 4 (c) 6 (d) 7
  16. 16.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 332 (b) 391 (c) 381 (d) 390
  17. 17.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  18. 18.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  19. 19.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 382 (c) 466 (d) 465
  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) 207 (b) 72 (c) 23 (d) 69
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 5 (b) 6 (c) 4 (d) 3
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 70? (a) 9 (b) 6 (c) 7 (d) 8
  23. 23.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) 11 (b) 33 (c) 36 (d) 99
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 2 (b) 3 (c) 5 (d) 4
  25. 25.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 18 (b) 20 (c) 9 (d) 19
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 4 (b) 2 (c) 5 (d) 3
  28. 28.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) 48 (b) 135 (c) 15 (d) 45
  29. 29.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) 30 (b) 33 (c) 90 (d) 10
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 13 (b) 3 (c) 14 (d) 15
  31. 31.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 248 (b) 265 (c) 255 (d) 264
  32. 32.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 4 (d) 6
  33. 33.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
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 84? (a) 19 (b) 8 (c) 20 (d) 18
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 6 (b) 5 (c) 7 (d) 4
  36. 36.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) 144 (b) 48 (c) 51 (d) 16
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 15 (b) 14 (c) 4 (d) 16
  38. 38.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 471 (c) 386 (d) 472
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 5 (b) 14 (c) 15 (d) 16
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 4 (b) 3 (c) 5 (d) 2

Answer key

  1. 6
  2. 75
  3. 7
  4. 24
  5. 7
  6. 19
  7. 5
  8. 18
  9. 9
  10. 14
  11. 2
  12. 51
  13. 228
  14. 19
  15. 6
  16. 390
  17. 6
  18. 8
  19. 465
  20. 69
  21. 5
  22. 8
  23. 33
  24. 4
  25. 2
  26. 19
  27. 4
  28. 45
  29. 30
  30. 14
  31. 264
  32. 5
  33. 462
  34. 19
  35. 6
  36. 48
  37. 15
  38. 471
  39. 15
  40. 4

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