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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 828 · 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 11? (a) 7 (b) 12 (c) 9 (d) 8
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 5 (b) 4 (c) 7 (d) 6
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 2 (b) 3 (c) 1 (d) 4
  4. 4.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) 20 (c) 180 (d) 63
  5. 5.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  6. 6.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
  7. 7.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 146 (c) 155 (d) 164
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 58? (a) 16 (b) 15 (c) 17 (d) 5
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 19 (b) 20 (c) 9 (d) 21
  10. 10.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 390 (c) 338 (d) 399
  11. 11.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 11 (d) 10
  12. 12.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) 63 (b) 189 (c) 21 (d) 66
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 12 (b) 14 (c) 13 (d) 3
  14. 14.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  15. 15.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 288 (c) 279 (d) 289
  16. 16.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 258 (c) 267 (d) 268
  17. 17.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 30 (c) 40 (d) 39
  18. 18.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) 12 (b) 36 (c) 39 (d) 108
  19. 19.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  20. 20.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
  21. 21.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) 7 (c) 63 (d) 21
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 75? (a) 5 (b) 6 (c) 8 (d) 7
  23. 23.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 282 (c) 316 (d) 315
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 18 (b) 19 (c) 7 (d) 17
  25. 25.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 7 (b) 8 (c) 9 (d) 6
  27. 27.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 165 (c) 166 (d) 156
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 4 (b) 2 (c) 1 (d) 3
  29. 29.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 202 (c) 192 (d) 206
  30. 30.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) 6 (c) 54 (d) 21
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 11 (b) 13 (c) 14 (d) 9
  32. 32.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  33. 33.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 577 (b) 567 (c) 456 (d) 576
  34. 34.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 178 (c) 187 (d) 196
  35. 35.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  36. 36.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  37. 37.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 4 (d) 10
  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) 54 (b) 18 (c) 57 (d) 162
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 17 (b) 18 (c) 7 (d) 19
  40. 40.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 588 (b) 597 (c) 598 (d) 470

Answer key

  1. 8
  2. 6
  3. 3
  4. 60
  5. 4
  6. 7
  7. 155
  8. 16
  9. 20
  10. 399
  11. 9
  12. 63
  13. 13
  14. 6
  15. 288
  16. 267
  17. 39
  18. 36
  19. 7
  20. 66
  21. 21
  22. 7
  23. 315
  24. 18
  25. 3
  26. 8
  27. 165
  28. 3
  29. 201
  30. 18
  31. 13
  32. 2
  33. 576
  34. 187
  35. 2
  36. 5
  37. 3
  38. 54
  39. 18
  40. 597

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