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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 155 · 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 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 39 (c) 12 (d) 36
  2. 2.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 102 (c) 92 (d) 101
  3. 3.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 33 (c) 99 (d) 11
  4. 4.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 117 (c) 13 (d) 42
  5. 5.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 7 (d) 9
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 20 (b) 8 (c) 18 (d) 19
  7. 7.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) 72 (b) 24 (c) 75 (d) 216
  8. 8.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) 20 (c) 63 (d) 60
  9. 9.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 342 (c) 351 (d) 306
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 71? (a) 18 (b) 16 (c) 7 (d) 17
  11. 11.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 153 (b) 162 (c) 154 (d) 144
  12. 12.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 564 (c) 454 (d) 574
  13. 13.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) 72 (c) 24 (d) 27
  14. 14.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
  15. 15.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 314 (b) 363 (c) 354 (d) 364
  16. 16.The numbers 11 to 19 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) 135 (c) 45 (d) 48
  17. 17.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  18. 18.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) 22 (b) 69 (c) 198 (d) 66
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 15 (b) 17 (c) 16 (d) 5
  20. 20.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 10 (d) 9
  21. 21.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
  22. 22.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  23. 23.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
  24. 24.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
  25. 25.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 217 (c) 216 (d) 207
  26. 26.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) 63 (c) 189 (d) 66
  27. 27.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 544 (c) 434 (d) 534
  28. 28.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  29. 29.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 224 (b) 219 (c) 229 (d) 228
  30. 30.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 5 (d) 3
  31. 31.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 375 (b) 366 (c) 376 (d) 322
  32. 32.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  33. 33.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
  34. 34.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 18 (b) 20 (c) 8 (d) 19
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 10 (b) 9 (c) 13 (d) 12
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 14 (b) 15 (c) 16 (d) 4
  38. 38.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
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 15 (b) 5 (c) 16 (d) 17
  40. 40.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 172 (c) 190 (d) 181

Answer key

  1. 36
  2. 101
  3. 33
  4. 39
  5. 8
  6. 19
  7. 72
  8. 60
  9. 351
  10. 17
  11. 153
  12. 573
  13. 24
  14. 9
  15. 363
  16. 45
  17. 3
  18. 66
  19. 16
  20. 8
  21. 5
  22. 6
  23. 2
  24. 57
  25. 216
  26. 63
  27. 543
  28. 5
  29. 228
  30. 4
  31. 375
  32. 6
  33. 9
  34. 7
  35. 19
  36. 12
  37. 15
  38. 51
  39. 16
  40. 181

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