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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 810 · 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.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 37 (b) 46 (c) 28 (d) 38
  2. 2.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 309 (b) 318 (c) 319 (d) 284
  3. 3.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 2 (d) 4
  4. 4.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  5. 5.The numbers 3 to 11 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) 21 (c) 7 (d) 63
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 1 (b) 2 (c) 4 (d) 3
  7. 7.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) 54 (c) 6 (d) 21
  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) 306 (b) 297 (c) 276 (d) 307
  9. 9.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) 162 (b) 57 (c) 18 (d) 54
  10. 10.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 27 (c) 72 (d) 24
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 73? (a) 9 (b) 7 (c) 11 (d) 12
  12. 12.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) 20 (b) 60 (c) 63 (d) 180
  13. 13.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  14. 14.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) 39 (c) 12 (d) 108
  15. 15.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 13 (c) 42 (d) 39
  16. 16.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  17. 17.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) 11 (b) 33 (c) 99 (d) 36
  18. 18.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 56? (a) 4 (b) 7 (c) 6 (d) 5
  20. 20.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  21. 21.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) 144 (d) 48
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 2 (b) 4 (c) 1 (d) 3
  23. 23.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 169 (b) 178 (c) 160 (d) 170
  24. 24.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) 72 (b) 24 (c) 75 (d) 216
  25. 25.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 579 (c) 580 (d) 458
  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) 126 (b) 45 (c) 14 (d) 42
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 19 (b) 8 (c) 17 (d) 18
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 4 (b) 2 (c) 5 (d) 3
  29. 29.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 6 (d) 15
  30. 30.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 223 (b) 220 (c) 222 (d) 213
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 19 (b) 8 (c) 18 (d) 17
  32. 32.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 492 (c) 501 (d) 502
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 18 (b) 20 (c) 8 (d) 19
  34. 34.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
  35. 35.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) 9 (b) 27 (c) 30 (d) 81
  36. 36.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) 23 (b) 72 (c) 69 (d) 207
  37. 37.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 41 (b) 32 (c) 42 (d) 50
  38. 38.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 147 (b) 148 (c) 138 (d) 156
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 19 (b) 21 (c) 20 (d) 9
  40. 40.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 173 (b) 182 (c) 174 (d) 164

Answer key

  1. 37
  2. 318
  3. 3
  4. 9
  5. 21
  6. 3
  7. 18
  8. 306
  9. 54
  10. 24
  11. 11
  12. 60
  13. 3
  14. 36
  15. 39
  16. 2
  17. 33
  18. 8
  19. 6
  20. 8
  21. 48
  22. 3
  23. 169
  24. 72
  25. 579
  26. 42
  27. 18
  28. 4
  29. 5
  30. 222
  31. 18
  32. 501
  33. 19
  34. 6
  35. 27
  36. 69
  37. 41
  38. 147
  39. 20
  40. 173

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