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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 931 · 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 10? (a) 11 (b) 10 (c) 9 (d) 8
  2. 2.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) 57 (d) 162
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 45? (a) 3 (b) 2 (c) 5 (d) 4
  4. 4.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 72 (c) 90 (d) 81
  5. 5.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 294 (c) 274 (d) 304
  6. 6.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) 99 (d) 36
  7. 7.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) 168 (c) 167 (d) 158
  8. 8.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 276 (c) 306 (d) 307
  9. 9.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) 10 (b) 90 (c) 33 (d) 30
  10. 10.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 4 (b) 11 (c) 10 (d) 12
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 6 (b) 16 (c) 17 (d) 18
  13. 13.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) 60 (b) 63 (c) 20 (d) 180
  14. 14.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 5 (b) 4 (c) 3 (d) 2
  16. 16.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) 72 (d) 24
  17. 17.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 537 (c) 547 (d) 546
  18. 18.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 7 (d) 12
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 15 (d) 14
  20. 20.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  21. 21.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 420 (c) 513 (d) 523
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 9 (b) 20 (c) 18 (d) 19
  23. 23.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  24. 24.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) 81 (b) 30 (c) 27 (d) 9
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 2 (d) 3
  26. 26.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 164 (c) 154 (d) 163
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 95? (a) 18 (b) 9 (c) 20 (d) 19
  28. 28.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 108 (c) 118 (d) 117
  29. 29.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 309 (c) 284 (d) 319
  30. 30.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 10 (d) 11
  31. 31.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 108 (c) 12 (d) 39
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 59? (a) 16 (b) 15 (c) 17 (d) 5
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 13 (b) 14 (c) 8 (d) 11
  34. 34.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 114 (c) 123 (d) 124
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 8 (b) 6 (c) 7 (d) 5
  36. 36.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) 198 (b) 22 (c) 69 (d) 66
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 3 (b) 4 (c) 5 (d) 6
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 17 (b) 19 (c) 18 (d) 7
  39. 39.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) 15 (c) 45 (d) 18
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 10 (b) 4 (c) 11 (d) 9

Answer key

  1. 9
  2. 54
  3. 4
  4. 81
  5. 303
  6. 33
  7. 167
  8. 306
  9. 30
  10. 2
  11. 11
  12. 17
  13. 60
  14. 6
  15. 4
  16. 72
  17. 546
  18. 8
  19. 15
  20. 3
  21. 522
  22. 19
  23. 2
  24. 27
  25. 3
  26. 163
  27. 19
  28. 117
  29. 318
  30. 9
  31. 36
  32. 16
  33. 13
  34. 123
  35. 7
  36. 66
  37. 5
  38. 18
  39. 15
  40. 10

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