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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 709 · 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 16? (a) 2 (b) 17 (c) 4 (d) 3
  2. 2.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 81 (b) 90 (c) 82 (d) 72
  3. 3.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 1 (d) 3
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 5 (b) 7 (c) 8 (d) 6
  5. 5.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 494 (b) 633 (c) 634 (d) 624
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 20 (b) 19 (c) 21 (d) 9
  7. 7.The numbers 11 to 19 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) 45 (c) 135 (d) 48
  8. 8.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
  9. 9.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 9 (d) 10
  10. 10.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 349 (c) 348 (d) 304
  11. 11.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 376 (c) 456 (d) 457
  12. 12.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 278 (b) 309 (c) 310 (d) 300
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 17 (b) 16 (c) 18 (d) 7
  14. 14.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 6 (d) 10
  15. 15.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  16. 16.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 380 (b) 463 (c) 453 (d) 462
  17. 17.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  18. 18.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) 57 (b) 171 (c) 19 (d) 60
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 9 (b) 13 (c) 14 (d) 11
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 17 (b) 8 (c) 19 (d) 18
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 66? (a) 14 (b) 6 (c) 15 (d) 13
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 13 (b) 12 (c) 11 (d) 3
  23. 23.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  24. 24.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) 27 (d) 24
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 15 (b) 17 (c) 5 (d) 16
  26. 26.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
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 5 (b) 15 (c) 17 (d) 16
  28. 28.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 376 (c) 322 (d) 375
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 14 (b) 15 (c) 4 (d) 16
  30. 30.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) 24 (b) 216 (c) 75 (d) 72
  31. 31.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
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 56? (a) 5 (b) 3 (c) 4 (d) 6
  33. 33.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 445 (c) 368 (d) 435
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 3 (b) 5 (c) 4 (d) 6
  35. 35.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) 51 (b) 17 (c) 54 (d) 153
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 86? (a) 8 (b) 20 (c) 19 (d) 18
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 16 (b) 18 (c) 17 (d) 6
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 17 (b) 16 (c) 18 (d) 7
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 20 (b) 19 (c) 8 (d) 18
  40. 40.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 180 (c) 190 (d) 198

Answer key

  1. 3
  2. 81
  3. 2
  4. 7
  5. 633
  6. 20
  7. 45
  8. 8
  9. 9
  10. 348
  11. 456
  12. 309
  13. 17
  14. 5
  15. 5
  16. 462
  17. 9
  18. 57
  19. 13
  20. 18
  21. 14
  22. 12
  23. 4
  24. 24
  25. 16
  26. 33
  27. 16
  28. 375
  29. 15
  30. 72
  31. 42
  32. 5
  33. 444
  34. 5
  35. 51
  36. 19
  37. 17
  38. 17
  39. 19
  40. 189

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