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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 937 · 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.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) 54 (d) 6
  2. 2.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 150 (c) 158 (d) 149
  3. 3.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 18 (b) 7 (c) 19 (d) 17
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 15 (b) 16 (c) 4 (d) 14
  7. 7.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 87 (c) 78 (d) 88
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 17 (b) 7 (c) 18 (d) 16
  9. 9.The numbers 12 to 20 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) 16 (c) 48 (d) 144
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 4 (b) 14 (c) 15 (d) 13
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 76? (a) 8 (b) 7 (c) 6 (d) 5
  12. 12.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 115 (b) 124 (c) 106 (d) 116
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 33? (a) 3 (b) 7 (c) 8 (d) 9
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 64? (a) 6 (b) 7 (c) 5 (d) 4
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 13 (b) 15 (c) 3 (d) 14
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 17 (b) 16 (c) 18 (d) 7
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 3 (b) 9 (c) 11 (d) 10
  18. 18.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 459 (c) 450 (d) 378
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 16 (b) 7 (c) 18 (d) 17
  20. 20.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 459 (c) 469 (d) 468
  21. 21.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 60? (a) 15 (b) 6 (c) 16 (d) 17
  23. 23.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) 33 (b) 10 (c) 30 (d) 90
  24. 24.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  25. 25.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  26. 26.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 42 (c) 41 (d) 32
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 1 (b) 2 (c) 4 (d) 3
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 4 (b) 6 (c) 3 (d) 5
  29. 29.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
  30. 30.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 339 (c) 340 (d) 298
  31. 31.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 259 (b) 244 (c) 258 (d) 249
  32. 32.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 238 (c) 250 (d) 240
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 18 (b) 6 (c) 16 (d) 17
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 13 (b) 3 (c) 14 (d) 15
  35. 35.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 266 (b) 291 (c) 292 (d) 282
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 3 (b) 5 (c) 6 (d) 4
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 51? (a) 16 (b) 15 (c) 5 (d) 14
  38. 38.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 452 (c) 571 (d) 570
  39. 39.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 45 (c) 54 (d) 46
  40. 40.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18

Answer key

  1. 18
  2. 149
  3. 9
  4. 18
  5. 6
  6. 15
  7. 87
  8. 17
  9. 48
  10. 14
  11. 7
  12. 115
  13. 8
  14. 6
  15. 14
  16. 17
  17. 10
  18. 459
  19. 17
  20. 468
  21. 7
  22. 16
  23. 30
  24. 2
  25. 4
  26. 41
  27. 3
  28. 5
  29. 4
  30. 339
  31. 258
  32. 249
  33. 17
  34. 14
  35. 291
  36. 5
  37. 15
  38. 570
  39. 45
  40. 2

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