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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 201 · 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 2? (a) 2 (b) 10 (c) 3 (d) 1
  2. 2.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) 23 (b) 69 (c) 72 (d) 207
  3. 3.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 81 (c) 27 (d) 9
  4. 4.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 192 (c) 174 (d) 183
  5. 5.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) 19 (b) 171 (c) 57 (d) 60
  6. 6.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 445 (b) 435 (c) 444 (d) 368
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 8 (b) 19 (c) 18 (d) 20
  8. 8.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  9. 9.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
  10. 10.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  11. 11.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 15 (b) 13 (c) 14 (d) 3
  13. 13.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) 135 (b) 45 (c) 15 (d) 48
  14. 14.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 138 (c) 120 (d) 129
  15. 15.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 600 (b) 478 (c) 610 (d) 609
  16. 16.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 7 (d) 9
  17. 17.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 541 (b) 531 (c) 540 (d) 432
  18. 18.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 459 (c) 469 (d) 468
  19. 19.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 189 (c) 199 (d) 198
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 18 (b) 19 (c) 7 (d) 17
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 80? (a) 8 (b) 17 (c) 18 (d) 19
  22. 22.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 612 (c) 603 (d) 613
  23. 23.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) 17 (c) 153 (d) 51
  24. 24.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) 36 (d) 11
  25. 25.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) 18 (b) 54 (c) 162 (d) 57
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 19 (d) 21
  27. 27.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 9 (d) 12
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 75? (a) 18 (b) 7 (c) 17 (d) 16
  29. 29.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 146 (c) 145 (d) 136
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 4 (b) 14 (c) 16 (d) 15
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 7 (b) 19 (c) 17 (d) 18
  32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 17 (b) 7 (c) 16 (d) 15
  33. 33.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) 5 (c) 15 (d) 18
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 68? (a) 7 (b) 5 (c) 8 (d) 6
  35. 35.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 451 (c) 450 (d) 441
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 16 (b) 17 (c) 18 (d) 6
  37. 37.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) 63 (c) 180 (d) 20
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 14 (b) 15 (c) 4 (d) 16
  39. 39.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  40. 40.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8

Answer key

  1. 2
  2. 69
  3. 27
  4. 183
  5. 57
  6. 444
  7. 19
  8. 4
  9. 3
  10. 6
  11. 4
  12. 14
  13. 45
  14. 129
  15. 609
  16. 8
  17. 540
  18. 468
  19. 198
  20. 18
  21. 18
  22. 612
  23. 51
  24. 33
  25. 54
  26. 20
  27. 8
  28. 17
  29. 145
  30. 15
  31. 18
  32. 16
  33. 15
  34. 7
  35. 450
  36. 17
  37. 60
  38. 15
  39. 9
  40. 9

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