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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 463 · 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 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 398 (b) 489 (c) 480 (d) 490
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 3 (b) 6 (c) 7 (d) 4
  3. 3.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 212 (b) 210 (c) 211 (d) 201
  4. 4.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
  5. 5.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 4 (d) 3
  6. 6.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) 21 (b) 18 (c) 6 (d) 54
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 18 (b) 8 (c) 19 (d) 20
  8. 8.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 306 (c) 276 (d) 307
  9. 9.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 394 (c) 334 (d) 393
  10. 10.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 421 (c) 411 (d) 420
  11. 11.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 7 (d) 6
  12. 12.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
  13. 13.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  14. 14.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) 15 (b) 18 (c) 5 (d) 45
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 20 (b) 18 (c) 8 (d) 19
  16. 16.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) 75 (c) 24 (d) 216
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 15 (b) 17 (c) 16 (d) 6
  18. 18.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 3 (b) 15 (c) 13 (d) 14
  20. 20.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) 171 (b) 57 (c) 60 (d) 19
  21. 21.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 8 (b) 18 (c) 19 (d) 20
  23. 23.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 35 (b) 26 (c) 44 (d) 36
  24. 24.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 224 (c) 229 (d) 228
  25. 25.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 586 (c) 462 (d) 576
  26. 26.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) 117 (b) 13 (c) 42 (d) 39
  27. 27.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 28 (c) 38 (d) 37
  28. 28.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 10 (d) 7
  29. 29.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
  30. 30.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 414 (c) 405 (d) 415
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 3 (b) 15 (c) 13 (d) 14
  32. 32.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 471 (b) 481 (c) 392 (d) 480
  33. 33.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 162 (c) 171 (d) 180
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 6 (b) 4 (c) 7 (d) 5
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 93? (a) 19 (b) 20 (c) 18 (d) 9
  36. 36.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 3 (b) 4 (c) 2 (d) 1
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 83? (a) 8 (b) 17 (c) 18 (d) 19
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 4 (b) 15 (c) 13 (d) 14
  40. 40.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 375 (c) 385 (d) 328

Answer key

  1. 489
  2. 6
  3. 210
  4. 2
  5. 4
  6. 18
  7. 19
  8. 306
  9. 393
  10. 420
  11. 6
  12. 8
  13. 7
  14. 15
  15. 19
  16. 72
  17. 16
  18. 3
  19. 14
  20. 57
  21. 7
  22. 19
  23. 35
  24. 228
  25. 585
  26. 39
  27. 37
  28. 6
  29. 4
  30. 414
  31. 14
  32. 480
  33. 171
  34. 6
  35. 19
  36. 3
  37. 3
  38. 18
  39. 14
  40. 384

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