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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 126 · 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 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 625 (b) 624 (c) 615 (d) 488
  2. 2.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) 63 (b) 20 (c) 60 (d) 180
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 66? (a) 6 (b) 18 (c) 17 (d) 16
  4. 4.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
  5. 5.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) 45 (c) 5 (d) 18
  6. 6.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) 14 (c) 45 (d) 126
  7. 7.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) 27 (d) 24
  8. 8.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 6 (d) 14
  9. 9.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 304 (c) 339 (d) 349
  10. 10.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) 18 (b) 54 (c) 6 (d) 21
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 2 (b) 3 (c) 4 (d) 5
  12. 12.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 20 (b) 19 (c) 18 (d) 9
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 20 (b) 19 (c) 8 (d) 18
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 11 (b) 9 (c) 8 (d) 10
  16. 16.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) 153 (b) 17 (c) 51 (d) 54
  17. 17.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 9 (d) 12
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 83? (a) 8 (b) 20 (c) 18 (d) 19
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 57? (a) 14 (b) 15 (c) 5 (d) 13
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 92? (a) 21 (b) 9 (c) 20 (d) 19
  21. 21.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 528 (c) 538 (d) 537
  22. 22.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 164 (c) 174 (d) 173
  23. 23.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) 81 (c) 30 (d) 27
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 8 (b) 18 (c) 19 (d) 17
  25. 25.The numbers 18 to 26 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) 22 (c) 198 (d) 66
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 2 (b) 4 (c) 1 (d) 3
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 19 (b) 20 (c) 18 (d) 9
  28. 28.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) 21 (b) 24 (c) 63 (d) 7
  29. 29.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 10 (d) 1
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 6 (b) 7 (c) 9 (d) 8
  31. 31.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 243 (c) 253 (d) 240
  32. 32.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) 72 (d) 23
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 55? (a) 17 (b) 16 (c) 15 (d) 5
  34. 34.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 15 (d) 6
  35. 35.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 295 (c) 268 (d) 285
  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) 434 (b) 543 (c) 544 (d) 534
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 19 (b) 21 (c) 9 (d) 20
  38. 38.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
  39. 39.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 223 (c) 222 (d) 213
  40. 40.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) 72 (c) 80 (d) 62

Answer key

  1. 624
  2. 60
  3. 17
  4. 2
  5. 15
  6. 42
  7. 24
  8. 6
  9. 348
  10. 18
  11. 4
  12. 7
  13. 19
  14. 19
  15. 10
  16. 51
  17. 8
  18. 19
  19. 14
  20. 20
  21. 537
  22. 173
  23. 27
  24. 18
  25. 66
  26. 3
  27. 19
  28. 21
  29. 2
  30. 8
  31. 252
  32. 69
  33. 16
  34. 5
  35. 294
  36. 543
  37. 20
  38. 9
  39. 222
  40. 71

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