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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 294 · 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 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
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 3 (b) 2 (c) 4 (d) 5
  3. 3.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 24 (c) 34 (d) 33
  4. 4.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 154 (c) 146 (d) 145
  5. 5.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 8 (d) 13
  6. 6.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 537 (c) 546 (d) 547
  7. 7.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 349 (b) 348 (c) 304 (d) 339
  8. 8.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 151 (b) 152 (c) 160 (d) 142
  9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 3 (b) 2 (c) 4 (d) 5
  10. 10.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) 69 (b) 23 (c) 72 (d) 207
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 97? (a) 20 (b) 19 (c) 9 (d) 21
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 16 (b) 13 (c) 15 (d) 8
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 9 (d) 8
  14. 14.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
  15. 15.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 502 (c) 406 (d) 501
  16. 16.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 165 (b) 174 (c) 156 (d) 166
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 1 (b) 2 (c) 3 (d) 4
  18. 18.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) 16 (b) 48 (c) 51 (d) 144
  19. 19.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  20. 20.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) 18 (b) 57 (c) 54 (d) 162
  21. 21.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 258 (c) 244 (d) 259
  22. 22.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  23. 23.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) 45 (b) 5 (c) 18 (d) 15
  24. 24.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 19 (b) 9 (c) 20 (d) 21
  26. 26.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  27. 27.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 340 (b) 402 (c) 393 (d) 403
  28. 28.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 214 (b) 204 (c) 213 (d) 321
  29. 29.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 631 (b) 621 (c) 630 (d) 492
  30. 30.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
  31. 31.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 297 (c) 307 (d) 276
  32. 32.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) 198 (c) 69 (d) 66
  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) 6 (b) 54 (c) 21 (d) 18
  34. 34.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) 186 (c) 177 (d) 168
  35. 35.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 229 (c) 219 (d) 224
  36. 36.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 595 (c) 585 (d) 468
  37. 37.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) 7 (c) 21 (d) 63
  38. 38.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 525 (b) 526 (c) 422 (d) 516
  39. 39.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) 42 (b) 13 (c) 117 (d) 39
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 19 (b) 9 (c) 18 (d) 20

Answer key

  1. 63
  2. 4
  3. 33
  4. 145
  5. 7
  6. 546
  7. 348
  8. 151
  9. 4
  10. 69
  11. 20
  12. 15
  13. 8
  14. 4
  15. 501
  16. 165
  17. 3
  18. 48
  19. 3
  20. 54
  21. 258
  22. 3
  23. 15
  24. 5
  25. 20
  26. 6
  27. 402
  28. 213
  29. 630
  30. 24
  31. 306
  32. 66
  33. 18
  34. 177
  35. 228
  36. 594
  37. 21
  38. 525
  39. 39
  40. 19

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