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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 348 · 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 5? (a) 4 (b) 5 (c) 6 (d) 10
  2. 2.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) 16 (b) 51 (c) 48 (d) 144
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 17 (b) 6 (c) 16 (d) 15
  4. 4.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
  5. 5.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
  6. 6.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
  7. 7.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
  8. 8.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 517 (b) 507 (c) 516 (d) 416
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 9 (b) 19 (c) 16 (d) 18
  10. 10.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
  11. 11.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) 6 (b) 18 (c) 21 (d) 54
  12. 12.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 162 (c) 144 (d) 153
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 4 (b) 2 (c) 1 (d) 3
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 14 (b) 13 (c) 15 (d) 3
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 84? (a) 20 (b) 19 (c) 8 (d) 18
  16. 16.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 585 (c) 586 (d) 576
  17. 17.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) 126 (c) 42 (d) 14
  18. 18.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 81 (c) 72 (d) 82
  19. 19.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) 72 (b) 207 (c) 23 (d) 69
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 10 (b) 7 (c) 6 (d) 9
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 18 (b) 16 (c) 17 (d) 7
  23. 23.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
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 16 (b) 18 (c) 7 (d) 17
  25. 25.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 300 (c) 291 (d) 272
  26. 26.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) 523 (d) 522
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 66? (a) 7 (b) 5 (c) 6 (d) 4
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 10 (b) 9 (c) 7 (d) 8
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 96? (a) 16 (b) 9 (c) 17 (d) 14
  30. 30.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 141 (b) 150 (c) 132 (d) 142
  31. 31.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 218 (b) 219 (c) 220 (d) 210
  32. 32.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 366 (c) 376 (d) 375
  33. 33.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) 72 (c) 8 (d) 27
  34. 34.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  35. 35.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 157 (c) 148 (d) 158
  36. 36.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 138 (c) 130 (d) 129
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 18 (b) 19 (c) 17 (d) 7
  38. 38.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) 598 (c) 470 (d) 597
  39. 39.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  40. 40.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) 45 (b) 48 (c) 15 (d) 135

Answer key

  1. 5
  2. 48
  3. 16
  4. 8
  5. 54
  6. 15
  7. 4
  8. 516
  9. 18
  10. 7
  11. 18
  12. 153
  13. 3
  14. 14
  15. 19
  16. 585
  17. 42
  18. 81
  19. 69
  20. 4
  21. 9
  22. 17
  23. 36
  24. 17
  25. 300
  26. 522
  27. 6
  28. 9
  29. 16
  30. 141
  31. 219
  32. 375
  33. 24
  34. 2
  35. 157
  36. 129
  37. 18
  38. 597
  39. 5
  40. 45

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