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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 618 · 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.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 528 (b) 519 (c) 424 (d) 529
  2. 2.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) 63 (b) 180 (c) 20 (d) 60
  3. 3.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 392 (b) 481 (c) 471 (d) 480
  4. 4.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 224 (b) 228 (c) 219 (d) 229
  5. 5.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) 207 (c) 72 (d) 69
  6. 6.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 83? (a) 8 (b) 20 (c) 18 (d) 19
  8. 8.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) 90 (b) 10 (c) 33 (d) 30
  9. 9.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  10. 10.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 189 (b) 21 (c) 63 (d) 66
  11. 11.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) 39 (b) 42 (c) 13 (d) 117
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 18 (b) 7 (c) 19 (d) 17
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 2 (b) 5 (c) 3 (d) 4
  14. 14.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 601 (c) 600 (d) 472
  15. 15.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) 57 (b) 60 (c) 19 (d) 171
  16. 16.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 556 (b) 555 (c) 442 (d) 546
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 3 (b) 5 (c) 6 (d) 4
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 13 (b) 15 (c) 16 (d) 8
  19. 19.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 230 (b) 238 (c) 237 (d) 228
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 68? (a) 7 (b) 6 (c) 5 (d) 8
  21. 21.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 297 (c) 298 (d) 270
  22. 22.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 284 (b) 309 (c) 319 (d) 318
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 7 (b) 3 (c) 4 (d) 6
  24. 24.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 298 (c) 340 (d) 330
  25. 25.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 10 (d) 8
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 4 (b) 15 (c) 14 (d) 16
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 18 (d) 19
  28. 28.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 5 (b) 8 (c) 7 (d) 4
  30. 30.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) 17 (d) 54
  31. 31.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 36 (c) 45 (d) 54
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 18 (b) 17 (c) 16 (d) 6
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 59? (a) 16 (b) 17 (c) 5 (d) 15
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 6 (b) 3 (c) 4 (d) 5
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 7 (b) 4 (c) 5 (d) 6
  36. 36.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
  37. 37.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 5 (d) 15
  38. 38.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) 63 (b) 21 (c) 7 (d) 24
  39. 39.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) 81 (b) 9 (c) 27 (d) 30
  40. 40.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6

Answer key

  1. 528
  2. 60
  3. 480
  4. 228
  5. 69
  6. 6
  7. 19
  8. 30
  9. 7
  10. 63
  11. 39
  12. 18
  13. 4
  14. 600
  15. 57
  16. 555
  17. 5
  18. 15
  19. 237
  20. 7
  21. 297
  22. 318
  23. 6
  24. 339
  25. 9
  26. 15
  27. 19
  28. 8
  29. 7
  30. 51
  31. 45
  32. 17
  33. 16
  34. 5
  35. 6
  36. 2
  37. 5
  38. 21
  39. 27
  40. 5

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