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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 277 · 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.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) 27 (d) 30
  2. 2.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) 171 (b) 60 (c) 57 (d) 19
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 6 (b) 8 (c) 5 (d) 7
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 4 (b) 2 (c) 5 (d) 3
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 20 (b) 18 (c) 19 (d) 9
  6. 6.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) 16 (d) 51
  7. 7.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 5 (b) 4 (c) 3 (d) 2
  9. 9.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 13 (d) 8
  10. 10.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
  11. 11.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 40 (c) 58 (d) 49
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 74? (a) 19 (b) 18 (c) 7 (d) 17
  13. 13.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  14. 14.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  15. 15.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 11 (d) 8
  16. 16.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 303 (c) 304 (d) 274
  17. 17.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 123 (b) 124 (c) 114 (d) 132
  18. 18.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 5 (d) 15
  19. 19.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  20. 20.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 351 (c) 243 (d) 244
  21. 21.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) 72 (b) 207 (c) 23 (d) 69
  22. 22.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  23. 23.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 381 (c) 391 (d) 332
  24. 24.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
  25. 25.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) 75 (b) 72 (c) 24 (d) 216
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 19 (b) 8 (c) 18 (d) 17
  27. 27.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) 33 (b) 30 (c) 10 (d) 90
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 5 (b) 2 (c) 3 (d) 4
  29. 29.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) 178 (d) 177
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 13 (b) 15 (c) 4 (d) 14
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 2 (b) 4 (c) 3 (d) 5
  32. 32.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) 21 (b) 189 (c) 66 (d) 63
  33. 33.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 255 (c) 248 (d) 265
  34. 34.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 278 (b) 300 (c) 309 (d) 310
  35. 35.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 18 (d) 1
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 85? (a) 8 (b) 19 (c) 18 (d) 20
  37. 37.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 38 (c) 48 (d) 47
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 18 (b) 17 (c) 7 (d) 16
  39. 39.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
  40. 40.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 537 (b) 430 (c) 528 (d) 538

Answer key

  1. 27
  2. 57
  3. 7
  4. 4
  5. 19
  6. 48
  7. 8
  8. 4
  9. 7
  10. 24
  11. 49
  12. 18
  13. 2
  14. 5
  15. 9
  16. 303
  17. 123
  18. 5
  19. 4
  20. 243
  21. 69
  22. 4
  23. 390
  24. 465
  25. 72
  26. 18
  27. 30
  28. 4
  29. 177
  30. 14
  31. 4
  32. 63
  33. 264
  34. 309
  35. 2
  36. 19
  37. 47
  38. 17
  39. 42
  40. 537

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