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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 977 · 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 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) 57 (b) 171 (c) 60 (d) 19
  2. 2.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) 27 (b) 24 (c) 72 (d) 8
  3. 3.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 379 (b) 378 (c) 369 (d) 324
  4. 4.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
  5. 5.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 96 (c) 86 (d) 95
  6. 6.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) 54 (c) 18 (d) 57
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 20 (b) 18 (c) 19 (d) 8
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 60? (a) 17 (b) 15 (c) 6 (d) 16
  9. 9.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 292 (c) 266 (d) 282
  10. 10.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 577 (b) 567 (c) 456 (d) 576
  11. 11.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) 153 (d) 51
  12. 12.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 33 (b) 42 (c) 24 (d) 34
  13. 13.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 308 (c) 355 (d) 354
  14. 14.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) 144 (d) 51
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 15 (b) 16 (c) 14 (d) 4
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 82? (a) 19 (b) 17 (c) 8 (d) 18
  17. 17.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 168 (c) 186 (d) 177
  18. 18.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  19. 19.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 398 (c) 490 (d) 489
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 19 (d) 20
  21. 21.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) 21 (c) 54 (d) 6
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 64? (a) 5 (b) 6 (c) 7 (d) 4
  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) 207 (b) 69 (c) 23 (d) 72
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 4 (b) 3 (c) 6 (d) 5
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 92? (a) 20 (b) 9 (c) 19 (d) 18
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 1 (b) 4 (c) 2 (d) 3
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 17 (b) 15 (c) 16 (d) 5
  28. 28.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 326 (b) 372 (c) 381 (d) 382
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 7 (b) 10 (c) 6 (d) 9
  30. 30.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  31. 31.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 447 (c) 448 (d) 370
  32. 32.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 613 (c) 612 (d) 603
  33. 33.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) 288 (c) 279 (d) 264
  34. 34.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 216 (c) 225 (d) 226
  35. 35.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) 14 (c) 126 (d) 42
  36. 36.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  37. 37.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) 33 (c) 30 (d) 10
  38. 38.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 12 (d) 7
  39. 39.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  40. 40.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18

Answer key

  1. 57
  2. 24
  3. 378
  4. 3
  5. 95
  6. 54
  7. 19
  8. 16
  9. 291
  10. 576
  11. 51
  12. 33
  13. 354
  14. 48
  15. 15
  16. 18
  17. 177
  18. 4
  19. 489
  20. 20
  21. 18
  22. 6
  23. 69
  24. 5
  25. 19
  26. 3
  27. 16
  28. 381
  29. 9
  30. 7
  31. 447
  32. 612
  33. 288
  34. 225
  35. 42
  36. 8
  37. 30
  38. 8
  39. 9
  40. 2

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