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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 569 · 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 13? (a) 6 (b) 14 (c) 7 (d) 5
  2. 2.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 109 (b) 110 (c) 118 (d) 100
  3. 3.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 2 (d) 3
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 18 (b) 19 (c) 20 (d) 9
  5. 5.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 18 (d) 9
  7. 7.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 252 (c) 246 (d) 261
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 19 (b) 18 (c) 9 (d) 20
  9. 9.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 379 (b) 378 (c) 324 (d) 369
  10. 10.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) 189 (b) 63 (c) 21 (d) 66
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 62? (a) 4 (b) 6 (c) 7 (d) 5
  12. 12.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 273 (c) 264 (d) 254
  13. 13.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) 126 (b) 45 (c) 14 (d) 42
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 14 (b) 13 (c) 3 (d) 15
  15. 15.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 318 (c) 370 (d) 360
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 17 (b) 7 (c) 19 (d) 18
  17. 17.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  18. 18.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 7 (b) 5 (c) 6 (d) 8
  20. 20.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 199 (b) 204 (c) 189 (d) 198
  21. 21.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 126 (c) 108 (d) 117
  22. 22.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 4 (d) 15
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 19 (b) 21 (c) 20 (d) 9
  24. 24.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) 135 (c) 48 (d) 45
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 19 (b) 17 (c) 18 (d) 8
  26. 26.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 481 (b) 392 (c) 480 (d) 471
  27. 27.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  28. 28.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 82 (c) 81 (d) 72
  29. 29.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) 18 (c) 5 (d) 15
  30. 30.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
  31. 31.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 67 (c) 76 (d) 58
  32. 32.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  33. 33.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) 27 (c) 9 (d) 30
  34. 34.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 166 (c) 175 (d) 176
  35. 35.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) 18 (b) 21 (c) 6 (d) 54
  36. 36.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 5 (b) 3 (c) 2 (d) 4
  38. 38.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 282 (c) 292 (d) 266
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 15 (b) 5 (c) 16 (d) 14
  40. 40.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) 36 (b) 33 (c) 11 (d) 99

Answer key

  1. 6
  2. 109
  3. 2
  4. 19
  5. 9
  6. 19
  7. 261
  8. 19
  9. 378
  10. 63
  11. 6
  12. 273
  13. 42
  14. 14
  15. 369
  16. 18
  17. 5
  18. 2
  19. 7
  20. 198
  21. 117
  22. 5
  23. 20
  24. 45
  25. 18
  26. 480
  27. 3
  28. 81
  29. 15
  30. 66
  31. 67
  32. 4
  33. 27
  34. 175
  35. 18
  36. 6
  37. 4
  38. 291
  39. 15
  40. 33

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