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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 715 · 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.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 312 (c) 351 (d) 361
  2. 2.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) 66 (b) 63 (c) 189 (d) 21
  3. 3.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  4. 4.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 406 (c) 405 (d) 342
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 4 (b) 3 (c) 5 (d) 2
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 87? (a) 8 (b) 16 (c) 14 (d) 17
  7. 7.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) 101 (c) 102 (d) 92
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 15 (b) 14 (c) 16 (d) 5
  9. 9.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 168 (c) 176 (d) 167
  10. 10.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) 66 (c) 22 (d) 69
  11. 11.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) 5 (b) 18 (c) 15 (d) 45
  12. 12.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 279 (c) 280 (d) 270
  13. 13.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 7 (b) 9 (c) 8 (d) 10
  15. 15.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 137 (b) 138 (c) 128 (d) 146
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 17 (b) 5 (c) 16 (d) 15
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 3 (b) 6 (c) 4 (d) 5
  18. 18.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 607 (c) 606 (d) 476
  19. 19.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  20. 20.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 18 (b) 17 (c) 7 (d) 16
  22. 22.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 78 (c) 70 (d) 69
  23. 23.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 173 (c) 174 (d) 164
  24. 24.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
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 1 (b) 2 (c) 3 (d) 4
  26. 26.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 324 (c) 378 (d) 379
  27. 27.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 72? (a) 8 (b) 10 (c) 7 (d) 11
  29. 29.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
  30. 30.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 254 (b) 274 (c) 273 (d) 264
  31. 31.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) 72 (c) 8 (d) 24
  32. 32.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 15 (b) 3 (c) 13 (d) 14
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 3 (b) 4 (c) 5 (d) 2
  35. 35.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
  36. 36.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 109 (c) 110 (d) 118
  37. 37.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  38. 38.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) 282 (c) 292 (d) 266
  39. 39.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) 216 (b) 75 (c) 72 (d) 24
  40. 40.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) 144 (d) 51

Answer key

  1. 360
  2. 63
  3. 9
  4. 405
  5. 4
  6. 16
  7. 101
  8. 15
  9. 167
  10. 66
  11. 15
  12. 279
  13. 3
  14. 9
  15. 137
  16. 16
  17. 5
  18. 606
  19. 2
  20. 3
  21. 17
  22. 69
  23. 173
  24. 576
  25. 3
  26. 378
  27. 7
  28. 10
  29. 306
  30. 273
  31. 24
  32. 4
  33. 14
  34. 4
  35. 8
  36. 109
  37. 5
  38. 291
  39. 72
  40. 48

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