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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 120 · 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 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) 24 (c) 216 (d) 72
  2. 2.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) 198 (b) 69 (c) 66 (d) 22
  3. 3.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 355 (b) 308 (c) 354 (d) 345
  4. 4.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
  5. 5.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) 33 (d) 30
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 6 (b) 16 (c) 18 (d) 17
  7. 7.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) 126 (c) 42 (d) 14
  8. 8.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 640 (b) 630 (c) 639 (d) 498
  9. 9.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 369 (c) 360 (d) 370
  10. 10.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 17 (d) 4
  11. 11.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 5 (d) 14
  12. 12.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 198 (c) 189 (d) 190
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 19 (b) 18 (c) 17 (d) 8
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 1 (d) 3
  15. 15.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 428 (b) 525 (c) 535 (d) 534
  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) 54 (b) 17 (c) 153 (d) 51
  17. 17.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 398 (b) 480 (c) 490 (d) 489
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 18 (b) 16 (c) 17 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  20. 20.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  21. 21.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) 8 (b) 24 (c) 27 (d) 72
  22. 22.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
  23. 23.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) 57 (b) 54 (c) 162 (d) 18
  24. 24.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) 18 (b) 15 (c) 45 (d) 5
  25. 25.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
  26. 26.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 13 (b) 15 (c) 3 (d) 14
  28. 28.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 95 (b) 104 (c) 86 (d) 96
  29. 29.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 46 (c) 36 (d) 45
  30. 30.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 292 (c) 331 (d) 330
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 2 (b) 4 (c) 3 (d) 5
  32. 32.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) 30 (b) 27 (c) 81 (d) 9
  33. 33.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) 54 (b) 21 (c) 6 (d) 18
  34. 34.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 309 (b) 284 (c) 318 (d) 319
  35. 35.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 7 (b) 12 (c) 15 (d) 14
  37. 37.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4
  38. 38.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 55 (b) 46 (c) 56 (d) 64
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 7 (b) 17 (c) 18 (d) 19
  40. 40.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 442 (c) 432 (d) 366

Answer key

  1. 72
  2. 66
  3. 354
  4. 5
  5. 30
  6. 17
  7. 42
  8. 639
  9. 369
  10. 3
  11. 6
  12. 189
  13. 18
  14. 3
  15. 534
  16. 51
  17. 489
  18. 17
  19. 4
  20. 3
  21. 24
  22. 167
  23. 54
  24. 15
  25. 5
  26. 8
  27. 14
  28. 95
  29. 45
  30. 330
  31. 4
  32. 27
  33. 18
  34. 318
  35. 7
  36. 14
  37. 4
  38. 55
  39. 18
  40. 441

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