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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 584 · 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 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
  2. 2.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  3. 3.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 452 (b) 570 (c) 571 (d) 561
  4. 4.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 48 (c) 58 (d) 57
  5. 5.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
  6. 6.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) 198 (d) 199
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 99? (a) 9 (b) 21 (c) 19 (d) 20
  8. 8.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 66 (c) 56 (d) 65
  9. 9.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 80 (c) 79 (d) 70
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 6 (b) 8 (c) 7 (d) 5
  11. 11.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  12. 12.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 123 (c) 114 (d) 124
  13. 13.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  14. 14.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) 21 (b) 63 (c) 7 (d) 24
  15. 15.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 1 (b) 3 (c) 2 (d) 4
  17. 17.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  18. 18.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) 5 (b) 45 (c) 15 (d) 18
  19. 19.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 126 (c) 118 (d) 117
  20. 20.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 102 (c) 94 (d) 93
  21. 21.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 15 (d) 6
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 8 (b) 10 (c) 3 (d) 9
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 17 (b) 5 (c) 16 (d) 15
  24. 24.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 501 (b) 406 (c) 502 (d) 492
  25. 25.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) 51 (b) 16 (c) 144 (d) 48
  26. 26.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 308 (b) 345 (c) 354 (d) 355
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 9 (b) 20 (c) 19 (d) 21
  28. 28.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) 69 (b) 22 (c) 66 (d) 198
  29. 29.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 190 (c) 189 (d) 180
  30. 30.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
  31. 31.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) 72 (d) 8
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 6 (b) 17 (c) 18 (d) 16
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 4 (b) 6 (c) 3 (d) 5
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 16 (b) 6 (c) 18 (d) 17
  35. 35.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 142 (c) 141 (d) 150
  36. 36.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 116 (c) 134 (d) 125
  37. 37.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) 153 (b) 51 (c) 54 (d) 17
  38. 38.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 388 (c) 387 (d) 378
  39. 39.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 254 (c) 264 (d) 273
  40. 40.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 553 (b) 552 (c) 440 (d) 543

Answer key

  1. 57
  2. 2
  3. 570
  4. 57
  5. 3
  6. 198
  7. 20
  8. 65
  9. 79
  10. 7
  11. 5
  12. 123
  13. 4
  14. 21
  15. 9
  16. 3
  17. 2
  18. 15
  19. 117
  20. 93
  21. 5
  22. 9
  23. 16
  24. 501
  25. 48
  26. 354
  27. 20
  28. 66
  29. 189
  30. 3
  31. 24
  32. 17
  33. 5
  34. 17
  35. 141
  36. 125
  37. 51
  38. 387
  39. 273
  40. 552

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