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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 376 · 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 3? (a) 3 (b) 2 (c) 4 (d) 10
  2. 2.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 9 (d) 10
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 14 (b) 15 (c) 3 (d) 13
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 7 (b) 3 (c) 6 (d) 4
  5. 5.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 18 (b) 6 (c) 16 (d) 17
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 52? (a) 4 (b) 3 (c) 6 (d) 5
  8. 8.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 54 (c) 53 (d) 44
  9. 9.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  10. 10.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 55 (b) 46 (c) 64 (d) 56
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 3 (b) 2 (c) 1 (d) 4
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 13 (b) 14 (c) 15 (d) 3
  13. 13.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 272 (b) 291 (c) 301 (d) 300
  14. 14.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 150 (c) 158 (d) 149
  15. 15.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) 14 (b) 45 (c) 126 (d) 42
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 12 (b) 14 (c) 13 (d) 3
  17. 17.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 246 (c) 247 (d) 236
  18. 18.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 440 (c) 552 (d) 553
  19. 19.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 4 (d) 17
  20. 20.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) 7 (b) 21 (c) 24 (d) 63
  21. 21.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 480 (c) 398 (d) 489
  22. 22.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 104 (c) 112 (d) 103
  23. 23.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) 99 (b) 33 (c) 11 (d) 36
  24. 24.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 6 (d) 7
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 17 (b) 7 (c) 18 (d) 16
  26. 26.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  27. 27.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) 168 (c) 150 (d) 160
  28. 28.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 540 (b) 438 (c) 550 (d) 549
  29. 29.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 334 (c) 394 (d) 384
  30. 30.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) 18 (b) 15 (c) 45 (d) 5
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 12 (b) 8 (c) 10 (d) 13
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 13 (b) 3 (c) 15 (d) 14
  33. 33.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) 42 (b) 13 (c) 117 (d) 39
  34. 34.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) 54 (b) 18 (c) 6 (d) 21
  35. 35.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) 22 (b) 69 (c) 66 (d) 198
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 17 (b) 6 (c) 16 (d) 18
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 14 (b) 4 (c) 16 (d) 15
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 59? (a) 4 (b) 6 (c) 5 (d) 7
  39. 39.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
  40. 40.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 169 (c) 178 (d) 160

Answer key

  1. 3
  2. 9
  3. 14
  4. 6
  5. 4
  6. 17
  7. 5
  8. 53
  9. 8
  10. 55
  11. 3
  12. 14
  13. 300
  14. 149
  15. 42
  16. 13
  17. 246
  18. 552
  19. 3
  20. 21
  21. 489
  22. 103
  23. 33
  24. 7
  25. 17
  26. 5
  27. 159
  28. 549
  29. 393
  30. 15
  31. 12
  32. 14
  33. 39
  34. 18
  35. 66
  36. 17
  37. 15
  38. 6
  39. 6
  40. 169

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