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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 984 · 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 times is the digit 6 written when you write all the numbers from 1 to 31? (a) 1 (b) 3 (c) 2 (d) 4
  2. 2.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 189 (c) 180 (d) 198
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 19 (b) 21 (c) 9 (d) 20
  4. 4.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 436 (c) 362 (d) 426
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 15 (b) 16 (c) 4 (d) 14
  6. 6.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) 72 (c) 207 (d) 23
  7. 7.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) 54 (c) 6 (d) 18
  8. 8.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) 45 (b) 14 (c) 126 (d) 42
  9. 9.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  10. 10.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 18 (b) 17 (c) 6 (d) 16
  12. 12.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 459 (b) 468 (c) 384 (d) 469
  13. 13.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 76 (c) 84 (d) 75
  14. 14.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 146 (c) 156 (d) 155
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 91? (a) 9 (b) 18 (c) 19 (d) 20
  16. 16.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 72 (c) 62 (d) 71
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 17 (b) 15 (c) 6 (d) 16
  18. 18.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) 7 (b) 21 (c) 63 (d) 24
  19. 19.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
  20. 20.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  21. 21.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 403 (b) 402 (c) 393 (d) 340
  22. 22.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 19 (b) 21 (c) 20 (d) 9
  24. 24.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 302 (b) 345 (c) 346 (d) 336
  25. 25.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) 216 (d) 24
  26. 26.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 15 (d) 5
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 18 (b) 19 (c) 20 (d) 9
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 2 (b) 5 (c) 3 (d) 4
  30. 30.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 7 (d) 8
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 8 (b) 7 (c) 6 (d) 5
  32. 32.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 118 (c) 117 (d) 108
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 18 (b) 20 (c) 9 (d) 19
  34. 34.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 319 (b) 284 (c) 309 (d) 318
  35. 35.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 423 (c) 354 (d) 414
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 5 (b) 7 (c) 4 (d) 6
  37. 37.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 45 (b) 54 (c) 46 (d) 36
  38. 38.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) 307 (c) 276 (d) 306
  39. 39.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 445 (b) 435 (c) 368 (d) 444
  40. 40.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2

Answer key

  1. 3
  2. 189
  3. 20
  4. 435
  5. 15
  6. 69
  7. 18
  8. 42
  9. 8
  10. 3
  11. 17
  12. 468
  13. 75
  14. 155
  15. 19
  16. 71
  17. 16
  18. 21
  19. 57
  20. 3
  21. 402
  22. 9
  23. 20
  24. 345
  25. 72
  26. 5
  27. 2
  28. 19
  29. 4
  30. 7
  31. 7
  32. 117
  33. 19
  34. 318
  35. 423
  36. 6
  37. 45
  38. 306
  39. 444
  40. 2

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