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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 269 · 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 15? (a) 5 (b) 16 (c) 3 (d) 4
  2. 2.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) 30 (c) 10 (d) 90
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 13 (b) 14 (c) 5 (d) 12
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 4 (b) 5 (c) 3 (d) 6
  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) 498 (b) 489 (c) 404 (d) 499
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 14 (b) 15 (c) 16 (d) 4
  7. 7.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
  8. 8.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 10 (d) 7
  9. 9.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 591 (c) 601 (d) 600
  10. 10.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 244 (c) 243 (d) 234
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 7 (b) 17 (c) 18 (d) 19
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  13. 13.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) 16 (b) 51 (c) 48 (d) 144
  14. 14.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
  15. 15.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  16. 16.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 153 (b) 162 (c) 144 (d) 154
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 2 (b) 3 (c) 1 (d) 4
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 15 (b) 8 (c) 13 (d) 16
  19. 19.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 303 (c) 274 (d) 294
  20. 20.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 125 (c) 126 (d) 116
  21. 21.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
  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) 24 (b) 75 (c) 216 (d) 72
  23. 23.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 45 (c) 18 (d) 15
  24. 24.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 174 (c) 183 (d) 192
  25. 25.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  26. 26.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) 42 (b) 14 (c) 45 (d) 126
  27. 27.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
  28. 28.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 206 (b) 202 (c) 201 (d) 192
  29. 29.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) 54 (b) 153 (c) 51 (d) 17
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 13 (b) 14 (c) 15 (d) 3
  31. 31.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  32. 32.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 433 (b) 360 (c) 423 (d) 432
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 17 (b) 15 (c) 7 (d) 16
  34. 34.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 519 (c) 529 (d) 528
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 18 (b) 17 (c) 19 (d) 7
  36. 36.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) 571 (c) 561 (d) 570
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 21 (d) 19
  38. 38.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 54 (c) 162 (d) 57
  39. 39.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) 33 (b) 11 (c) 36 (d) 99
  40. 40.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 84 (c) 94 (d) 93

Answer key

  1. 4
  2. 30
  3. 13
  4. 5
  5. 498
  6. 15
  7. 5
  8. 6
  9. 600
  10. 243
  11. 18
  12. 5
  13. 48
  14. 7
  15. 4
  16. 153
  17. 3
  18. 15
  19. 303
  20. 125
  21. 2
  22. 72
  23. 15
  24. 183
  25. 6
  26. 42
  27. 9
  28. 201
  29. 51
  30. 14
  31. 2
  32. 432
  33. 16
  34. 528
  35. 18
  36. 570
  37. 20
  38. 54
  39. 33
  40. 93

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