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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 701 · 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 two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 85? (a) 15 (b) 8 (c) 12 (d) 14
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 16 (b) 15 (c) 14 (d) 5
  4. 4.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 356 (b) 427 (c) 417 (d) 426
  5. 5.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) 39 (b) 13 (c) 117 (d) 42
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 19 (b) 20 (c) 9 (d) 21
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 96? (a) 19 (b) 9 (c) 20 (d) 21
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 6 (b) 4 (c) 3 (d) 5
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 4 (b) 6 (c) 5 (d) 7
  10. 10.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 6 (d) 4
  11. 11.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 452 (b) 561 (c) 571 (d) 570
  12. 12.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 475 (b) 388 (c) 474 (d) 465
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 67? (a) 6 (b) 14 (c) 15 (d) 16
  14. 14.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 17 (b) 7 (c) 18 (d) 19
  16. 16.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) 69 (b) 22 (c) 66 (d) 198
  17. 17.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 318 (c) 369 (d) 360
  18. 18.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  19. 19.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
  20. 20.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 30 (c) 33 (d) 10
  21. 21.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 54 (c) 153 (d) 51
  22. 22.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 53 (b) 62 (c) 54 (d) 44
  23. 23.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 14 (b) 16 (c) 4 (d) 15
  25. 25.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) 18 (c) 21 (d) 54
  26. 26.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 253 (b) 240 (c) 252 (d) 243
  27. 27.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 386 (b) 472 (c) 462 (d) 471
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 64? (a) 6 (b) 4 (c) 5 (d) 7
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 21 (b) 19 (c) 20 (d) 9
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 97? (a) 18 (b) 19 (c) 9 (d) 20
  31. 31.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  32. 32.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) 27 (c) 24 (d) 72
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 18 (b) 17 (c) 19 (d) 7
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 79? (a) 17 (b) 19 (c) 7 (d) 18
  35. 35.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) 126 (b) 14 (c) 42 (d) 45
  36. 36.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) 21 (d) 189
  37. 37.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 505 (c) 504 (d) 495
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 16 (b) 15 (c) 17 (d) 5
  39. 39.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 588 (b) 589 (c) 464 (d) 579
  40. 40.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13

Answer key

  1. 7
  2. 14
  3. 15
  4. 426
  5. 39
  6. 20
  7. 20
  8. 5
  9. 6
  10. 5
  11. 570
  12. 474
  13. 15
  14. 2
  15. 18
  16. 66
  17. 369
  18. 9
  19. 33
  20. 30
  21. 51
  22. 53
  23. 4
  24. 15
  25. 18
  26. 252
  27. 471
  28. 6
  29. 20
  30. 19
  31. 3
  32. 24
  33. 18
  34. 18
  35. 42
  36. 63
  37. 504
  38. 16
  39. 588
  40. 7

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