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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 521 · 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 times is the digit 2 written when you write all the numbers from 1 to 40? (a) 15 (b) 13 (c) 14 (d) 4
  2. 2.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  3. 3.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 189 (c) 198 (d) 199
  4. 4.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) 39 (b) 117 (c) 13 (d) 42
  5. 5.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 238 (b) 240 (c) 250 (d) 249
  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) 240 (b) 252 (c) 243 (d) 253
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 3 (b) 4 (c) 6 (d) 5
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 75? (a) 14 (b) 7 (c) 11 (d) 13
  9. 9.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 555 (b) 448 (c) 564 (d) 565
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 10 (d) 6
  11. 11.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) 21 (b) 6 (c) 54 (d) 18
  12. 12.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
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 5 (b) 6 (c) 8 (d) 7
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 6 (b) 4 (c) 5 (d) 7
  15. 15.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) 54 (b) 51 (c) 17 (d) 153
  16. 16.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) 24 (c) 8 (d) 27
  17. 17.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 81 (c) 82 (d) 90
  18. 18.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 289 (b) 264 (c) 279 (d) 288
  19. 19.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) 5 (b) 18 (c) 15 (d) 45
  20. 20.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
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 75? (a) 6 (b) 5 (c) 8 (d) 7
  22. 22.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) 45 (b) 42 (c) 14 (d) 126
  23. 23.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
  24. 24.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) 63 (b) 66 (c) 189 (d) 21
  25. 25.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 15 (b) 6 (c) 16 (d) 17
  27. 27.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 71 (b) 62 (c) 72 (d) 80
  28. 28.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 14 (b) 9 (c) 11 (d) 13
  30. 30.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) 108 (b) 12 (c) 39 (d) 36
  31. 31.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 540 (c) 550 (d) 549
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 17 (b) 7 (c) 19 (d) 18
  33. 33.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 3 (b) 9 (c) 11 (d) 10
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 3 (b) 5 (c) 4 (d) 6
  36. 36.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 534 (c) 544 (d) 434
  37. 37.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) 48 (b) 16 (c) 51 (d) 144
  38. 38.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 21 (c) 7 (d) 24
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 94? (a) 21 (b) 20 (c) 9 (d) 19
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 16 (b) 14 (c) 4 (d) 15

Answer key

  1. 14
  2. 3
  3. 198
  4. 39
  5. 249
  6. 252
  7. 5
  8. 13
  9. 564
  10. 7
  11. 18
  12. 20
  13. 7
  14. 6
  15. 51
  16. 24
  17. 81
  18. 288
  19. 15
  20. 54
  21. 7
  22. 42
  23. 7
  24. 63
  25. 8
  26. 16
  27. 71
  28. 6
  29. 13
  30. 36
  31. 549
  32. 18
  33. 2
  34. 10
  35. 5
  36. 543
  37. 48
  38. 21
  39. 20
  40. 15

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