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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 705 · 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 3 written when you write all the numbers from 1 to 73? (a) 7 (b) 19 (c) 18 (d) 17
  2. 2.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 10 (d) 6
  3. 3.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
  4. 4.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) 63 (b) 60 (c) 180 (d) 20
  5. 5.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 498 (c) 499 (d) 404
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 3 (b) 6 (c) 4 (d) 5
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 5 (b) 2 (c) 4 (d) 3
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 18 (b) 17 (c) 6 (d) 16
  9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 73? (a) 7 (b) 17 (c) 16 (d) 18
  10. 10.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 167 (c) 158 (d) 168
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 3 (b) 4 (c) 2 (d) 1
  12. 12.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 409 (c) 344 (d) 399
  13. 13.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 276 (c) 267 (d) 277
  14. 14.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 621 (c) 612 (d) 622
  15. 15.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 556 (c) 442 (d) 555
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 65? (a) 5 (b) 6 (c) 4 (d) 7
  17. 17.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 258 (c) 267 (d) 250
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 9 (b) 6 (c) 5 (d) 8
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 19 (d) 18
  20. 20.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  21. 21.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) 11 (b) 99 (c) 36 (d) 33
  22. 22.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) 24 (d) 72
  23. 23.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 4 (d) 2
  24. 24.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 321 (c) 286 (d) 322
  25. 25.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 81 (c) 27 (d) 9
  26. 26.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
  27. 27.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 7 (b) 17 (c) 18 (d) 19
  29. 29.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 519 (b) 520 (c) 510 (d) 418
  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) 8 (b) 72 (c) 24 (d) 27
  31. 31.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 535 (c) 525 (d) 428
  32. 32.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 19 (b) 9 (c) 20 (d) 21
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 62? (a) 5 (b) 4 (c) 6 (d) 7
  35. 35.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 5 (b) 4 (c) 3 (d) 6
  37. 37.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 3 (b) 4 (c) 2 (d) 5
  39. 39.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) 21 (c) 54 (d) 18
  40. 40.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) 42 (c) 14 (d) 126

Answer key

  1. 18
  2. 7
  3. 3
  4. 60
  5. 498
  6. 5
  7. 4
  8. 17
  9. 17
  10. 167
  11. 3
  12. 408
  13. 276
  14. 621
  15. 555
  16. 6
  17. 267
  18. 8
  19. 19
  20. 9
  21. 33
  22. 72
  23. 3
  24. 321
  25. 27
  26. 8
  27. 6
  28. 18
  29. 519
  30. 24
  31. 534
  32. 5
  33. 20
  34. 6
  35. 8
  36. 5
  37. 5
  38. 4
  39. 18
  40. 42

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