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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 105 · 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.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) 10 (c) 90 (d) 30
  2. 2.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) 45 (c) 15 (d) 5
  3. 3.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  4. 4.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
  5. 5.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) 176 (c) 175 (d) 166
  6. 6.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 87 (b) 88 (c) 78 (d) 96
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 6 (b) 9 (c) 8 (d) 5
  8. 8.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  9. 9.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) 54 (b) 153 (c) 17 (d) 51
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 19 (b) 18 (c) 7 (d) 17
  11. 11.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 16 (b) 17 (c) 6 (d) 18
  13. 13.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 11 (d) 10
  14. 14.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 420 (c) 522 (d) 523
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 54? (a) 5 (b) 17 (c) 15 (d) 16
  16. 16.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 364 (c) 314 (d) 363
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 15 (b) 14 (c) 4 (d) 13
  18. 18.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 274 (c) 294 (d) 303
  19. 19.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) 39 (b) 108 (c) 12 (d) 36
  20. 20.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) 42 (b) 126 (c) 45 (d) 14
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 19 (b) 18 (c) 17 (d) 7
  22. 22.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 433 (b) 423 (c) 432 (d) 360
  23. 23.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 140 (c) 149 (d) 158
  24. 24.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 8 (d) 10
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 75? (a) 5 (b) 8 (c) 7 (d) 6
  26. 26.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
  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) 150 (b) 168 (c) 160 (d) 159
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 50? (a) 6 (b) 3 (c) 4 (d) 5
  29. 29.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 196 (c) 187 (d) 188
  30. 30.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) 45 (c) 48 (d) 135
  31. 31.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 338 (b) 400 (c) 390 (d) 399
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 20 (d) 19
  33. 33.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
  34. 34.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 501 (b) 412 (c) 511 (d) 510
  35. 35.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 85 (b) 94 (c) 76 (d) 86
  36. 36.The numbers 15 to 23 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) 57 (c) 171 (d) 19
  37. 37.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 61? (a) 6 (b) 7 (c) 4 (d) 5
  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) 66 (b) 198 (c) 22 (d) 69
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 81? (a) 17 (b) 19 (c) 18 (d) 8

Answer key

  1. 30
  2. 15
  3. 2
  4. 6
  5. 175
  6. 87
  7. 8
  8. 8
  9. 51
  10. 18
  11. 5
  12. 17
  13. 9
  14. 522
  15. 16
  16. 363
  17. 14
  18. 303
  19. 36
  20. 42
  21. 18
  22. 432
  23. 149
  24. 7
  25. 7
  26. 261
  27. 159
  28. 5
  29. 187
  30. 45
  31. 399
  32. 19
  33. 18
  34. 510
  35. 85
  36. 57
  37. 4
  38. 6
  39. 66
  40. 18

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