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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 869 · 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 12? (a) 7 (b) 8 (c) 13 (d) 6
  2. 2.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 460 (c) 459 (d) 378
  3. 3.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 159 (b) 160 (c) 150 (d) 168
  4. 4.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 69 (c) 72 (d) 23
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 6 (b) 4 (c) 5 (d) 3
  6. 6.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 238 (c) 228 (d) 230
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 4 (b) 2 (c) 3 (d) 5
  8. 8.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 14 (b) 5 (c) 15 (d) 16
  10. 10.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 186 (c) 177 (d) 168
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 4 (b) 14 (c) 16 (d) 15
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 97? (a) 9 (b) 21 (c) 19 (d) 20
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 2 (b) 4 (c) 3 (d) 5
  14. 14.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
  15. 15.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 232 (c) 226 (d) 231
  16. 16.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 152 (c) 143 (d) 144
  17. 17.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 134 (c) 125 (d) 126
  18. 18.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 446 (b) 562 (c) 561 (d) 552
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 9 (b) 21 (c) 19 (d) 20
  20. 20.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 525 (b) 428 (c) 535 (d) 534
  21. 21.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 3 (b) 12 (c) 11 (d) 13
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 17 (b) 7 (c) 19 (d) 18
  24. 24.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 7 (d) 8
  25. 25.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) 21 (c) 63 (d) 189
  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) 154 (b) 172 (c) 163 (d) 164
  27. 27.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) 180 (b) 20 (c) 60 (d) 63
  28. 28.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) 69 (c) 66 (d) 22
  29. 29.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 4 (b) 6 (c) 5 (d) 7
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 92? (a) 9 (b) 18 (c) 19 (d) 20
  32. 32.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) 45 (b) 5 (c) 18 (d) 15
  33. 33.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) 75 (b) 24 (c) 216 (d) 72
  34. 34.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 3 (d) 10
  35. 35.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  36. 36.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 466 (c) 465 (d) 382
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 4 (b) 6 (c) 5 (d) 3
  38. 38.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 232 (c) 231 (d) 241
  39. 39.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 7 (b) 18 (c) 17 (d) 19

Answer key

  1. 7
  2. 459
  3. 159
  4. 69
  5. 5
  6. 237
  7. 4
  8. 3
  9. 15
  10. 177
  11. 15
  12. 20
  13. 4
  14. 9
  15. 231
  16. 143
  17. 125
  18. 561
  19. 20
  20. 534
  21. 5
  22. 12
  23. 18
  24. 7
  25. 63
  26. 163
  27. 60
  28. 66
  29. 6
  30. 6
  31. 19
  32. 15
  33. 72
  34. 4
  35. 2
  36. 465
  37. 5
  38. 240
  39. 9
  40. 18

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