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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 657 · 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 16? (a) 3 (b) 2 (c) 4 (d) 17
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 50? (a) 3 (b) 6 (c) 4 (d) 5
  3. 3.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 10 (d) 8
  4. 4.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) 24 (b) 27 (c) 8 (d) 72
  5. 5.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) 108 (d) 12
  6. 6.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 45? (a) 2 (b) 4 (c) 3 (d) 5
  8. 8.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  9. 9.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 91 (b) 100 (c) 92 (d) 82
  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) 66 (b) 21 (c) 189 (d) 63
  11. 11.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
  12. 12.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 101 (b) 92 (c) 102 (d) 110
  13. 13.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
  14. 14.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 284 (b) 309 (c) 319 (d) 318
  15. 15.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 151 (c) 142 (d) 152
  16. 16.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 51 (c) 153 (d) 54
  17. 17.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) 180 (c) 63 (d) 60
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 18 (b) 19 (c) 17 (d) 8
  19. 19.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) 144 (b) 51 (c) 16 (d) 48
  20. 20.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) 15 (d) 5
  21. 21.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) 45 (b) 14 (c) 42 (d) 126
  22. 22.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 141 (c) 150 (d) 132
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 15 (b) 13 (c) 14 (d) 3
  24. 24.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  25. 25.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
  26. 26.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 346 (c) 412 (d) 402
  27. 27.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 30 (c) 90 (d) 10
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 20 (b) 8 (c) 19 (d) 18
  29. 29.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) 21 (b) 54 (c) 18 (d) 6
  30. 30.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 4 (b) 3 (c) 5 (d) 2
  32. 32.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 46 (c) 55 (d) 56
  33. 33.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 33 (b) 24 (c) 42 (d) 34
  34. 34.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  35. 35.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) 24 (b) 72 (c) 216 (d) 75
  36. 36.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 105 (b) 96 (c) 106 (d) 114
  37. 37.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 70 (c) 61 (d) 52
  38. 38.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 382 (c) 381 (d) 326
  39. 39.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) 66 (c) 69 (d) 22
  40. 40.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 339 (c) 330 (d) 340

Answer key

  1. 3
  2. 5
  3. 7
  4. 24
  5. 36
  6. 7
  7. 4
  8. 3
  9. 91
  10. 63
  11. 45
  12. 101
  13. 21
  14. 318
  15. 151
  16. 51
  17. 60
  18. 18
  19. 48
  20. 15
  21. 42
  22. 141
  23. 14
  24. 6
  25. 2
  26. 411
  27. 30
  28. 19
  29. 18
  30. 4
  31. 4
  32. 55
  33. 33
  34. 5
  35. 72
  36. 105
  37. 61
  38. 381
  39. 66
  40. 339

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