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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 340 · 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.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 9 (d) 11
  2. 2.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) 24 (b) 21 (c) 63 (d) 7
  3. 3.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) 23 (b) 207 (c) 72 (d) 69
  4. 4.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) 14 (b) 45 (c) 42 (d) 126
  5. 5.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
  6. 6.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 35 (c) 44 (d) 26
  7. 7.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) 60 (b) 171 (c) 19 (d) 57
  8. 8.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 294 (c) 304 (d) 303
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 5 (b) 4 (c) 3 (d) 6
  10. 10.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) 189 (b) 21 (c) 66 (d) 63
  11. 11.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  12. 12.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  13. 13.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 622 (b) 486 (c) 612 (d) 621
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 4 (b) 1 (c) 3 (d) 2
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 87? (a) 20 (b) 18 (c) 8 (d) 19
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 4 (b) 1 (c) 2 (d) 3
  17. 17.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) 72 (d) 27
  18. 18.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 164 (c) 154 (d) 163
  19. 19.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 150 (c) 142 (d) 141
  20. 20.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  21. 21.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
  22. 22.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 7 (d) 6
  23. 23.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 3 (d) 1
  24. 24.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
  25. 25.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 111 (b) 102 (c) 120 (d) 112
  26. 26.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) 21 (d) 6
  27. 27.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 405 (c) 396 (d) 342
  28. 28.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) 498 (d) 639
  29. 29.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 71? (a) 7 (b) 18 (c) 17 (d) 16
  31. 31.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) 180 (b) 63 (c) 60 (d) 20
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 54? (a) 5 (b) 16 (c) 17 (d) 15
  33. 33.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 309 (c) 319 (d) 284
  34. 34.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
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 19 (b) 18 (c) 20 (d) 8
  36. 36.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 20 (b) 9 (c) 18 (d) 19
  38. 38.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 453 (c) 444 (d) 374
  39. 39.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
  40. 40.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 4 (d) 2

Answer key

  1. 9
  2. 21
  3. 69
  4. 42
  5. 72
  6. 35
  7. 57
  8. 303
  9. 5
  10. 63
  11. 8
  12. 4
  13. 621
  14. 3
  15. 19
  16. 3
  17. 24
  18. 163
  19. 141
  20. 2
  21. 51
  22. 7
  23. 2
  24. 27
  25. 111
  26. 18
  27. 405
  28. 639
  29. 4
  30. 17
  31. 60
  32. 16
  33. 318
  34. 447
  35. 19
  36. 3
  37. 19
  38. 453
  39. 9
  40. 3

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