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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 593 · 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 13? (a) 7 (b) 6 (c) 14 (d) 5
  2. 2.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) 27 (c) 81 (d) 9
  3. 3.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 457 (c) 447 (d) 376
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 58? (a) 6 (b) 5 (c) 4 (d) 7
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 8 (b) 7 (c) 6 (d) 9
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 75? (a) 11 (b) 13 (c) 7 (d) 14
  7. 7.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) 30 (b) 10 (c) 33 (d) 90
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  9. 9.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 57 (b) 58 (c) 66 (d) 48
  10. 10.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) 78 (c) 88 (d) 96
  11. 11.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 66? (a) 7 (b) 5 (c) 6 (d) 4
  13. 13.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 117 (b) 126 (c) 108 (d) 118
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 7 (b) 18 (c) 17 (d) 19
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 78? (a) 18 (b) 7 (c) 19 (d) 17
  16. 16.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 7 (d) 9
  17. 17.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 45 (c) 46 (d) 36
  18. 18.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 2 (d) 17
  19. 19.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 124 (c) 142 (d) 133
  20. 20.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
  21. 21.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 544 (b) 434 (c) 534 (d) 543
  22. 22.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 429 (c) 364 (d) 439
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 16 (b) 14 (c) 15 (d) 4
  24. 24.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
  25. 25.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3
  26. 26.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 138 (c) 147 (d) 148
  27. 27.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 327 (c) 290 (d) 318
  28. 28.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 331 (b) 330 (c) 292 (d) 321
  29. 29.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 436 (c) 426 (d) 362
  30. 30.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 2 (d) 4
  31. 31.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) 57 (b) 18 (c) 162 (d) 54
  32. 32.The numbers 9 to 17 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) 117 (c) 13 (d) 39
  33. 33.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 16 (b) 18 (c) 6 (d) 17
  35. 35.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
  36. 36.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  37. 37.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) 75 (b) 216 (c) 72 (d) 24
  38. 38.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) 510 (d) 511
  39. 39.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 10 (d) 7
  40. 40.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) 48 (b) 16 (c) 144 (d) 51

Answer key

  1. 6
  2. 27
  3. 456
  4. 6
  5. 8
  6. 13
  7. 30
  8. 5
  9. 57
  10. 87
  11. 4
  12. 6
  13. 117
  14. 18
  15. 18
  16. 8
  17. 45
  18. 3
  19. 133
  20. 4
  21. 543
  22. 438
  23. 15
  24. 375
  25. 2
  26. 147
  27. 327
  28. 330
  29. 435
  30. 3
  31. 54
  32. 39
  33. 9
  34. 17
  35. 24
  36. 5
  37. 72
  38. 510
  39. 6
  40. 48

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