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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 924 · 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.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 167 (c) 176 (d) 158
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 4 (b) 15 (c) 16 (d) 14
  3. 3.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 186 (c) 177 (d) 178
  4. 4.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  6. 6.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) 9 (b) 27 (c) 30 (d) 81
  7. 7.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  8. 8.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 12 (d) 7
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 2 (b) 1 (c) 4 (d) 3
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 17 (b) 15 (c) 16 (d) 6
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 4 (b) 11 (c) 10 (d) 9
  12. 12.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) 19 (b) 57 (c) 60 (d) 171
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 19 (b) 17 (c) 18 (d) 7
  14. 14.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 333 (c) 334 (d) 294
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 7 (b) 18 (c) 17 (d) 19
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 14 (b) 16 (c) 4 (d) 15
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 5 (b) 2 (c) 4 (d) 3
  18. 18.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 420 (c) 523 (d) 522
  19. 19.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
  20. 20.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
  21. 21.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) 66 (b) 63 (c) 21 (d) 189
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 4 (b) 7 (c) 6 (d) 5
  23. 23.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) 69 (b) 207 (c) 23 (d) 72
  24. 24.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) 42 (c) 13 (d) 39
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 15 (b) 7 (c) 12 (d) 14
  26. 26.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 67? (a) 6 (b) 16 (c) 14 (d) 15
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 15 (b) 14 (c) 16 (d) 4
  29. 29.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 481 (b) 392 (c) 471 (d) 480
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 17 (b) 19 (c) 8 (d) 18
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 18 (b) 19 (c) 7 (d) 17
  32. 32.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 7 (d) 6
  33. 33.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 15 (d) 6
  34. 34.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 75 (c) 24 (d) 72
  35. 35.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) 7 (b) 63 (c) 21 (d) 24
  36. 36.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) 12 (b) 108 (c) 36 (d) 39
  37. 37.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 5 (b) 4 (c) 3 (d) 6
  39. 39.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) 90 (b) 10 (c) 30 (d) 33
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 8 (b) 9 (c) 6 (d) 7

Answer key

  1. 167
  2. 15
  3. 177
  4. 3
  5. 6
  6. 27
  7. 4
  8. 8
  9. 3
  10. 16
  11. 10
  12. 57
  13. 18
  14. 333
  15. 18
  16. 15
  17. 4
  18. 522
  19. 564
  20. 7
  21. 63
  22. 6
  23. 69
  24. 39
  25. 14
  26. 2
  27. 15
  28. 15
  29. 480
  30. 18
  31. 18
  32. 7
  33. 5
  34. 72
  35. 21
  36. 36
  37. 5
  38. 5
  39. 30
  40. 8

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