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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 81 · 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 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) 20 (b) 63 (c) 180 (d) 60
  2. 2.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 24 (b) 34 (c) 42 (d) 33
  3. 3.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) 42 (c) 14 (d) 126
  4. 4.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 66 (c) 76 (d) 75
  5. 5.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) 10 (b) 33 (c) 30 (d) 90
  6. 6.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) 11 (b) 36 (c) 99 (d) 33
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 2 (d) 3
  8. 8.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) 54 (b) 6 (c) 18 (d) 21
  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) 80 (b) 70 (c) 79 (d) 88
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  11. 11.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 12 (d) 9
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
  13. 13.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 10 (d) 11
  14. 14.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 6 (d) 15
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 5 (b) 3 (c) 4 (d) 2
  16. 16.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 427 (b) 426 (c) 417 (d) 356
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 85? (a) 7 (b) 9 (c) 8 (d) 6
  18. 18.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5
  19. 19.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) 24 (c) 21 (d) 7
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 18 (b) 7 (c) 16 (d) 17
  21. 21.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 3 (d) 16
  22. 22.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 69 (b) 78 (c) 60 (d) 70
  23. 23.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 225 (c) 222 (d) 216
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 14 (b) 15 (c) 4 (d) 16
  25. 25.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) 66 (c) 21 (d) 63
  26. 26.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 397 (b) 396 (c) 336 (d) 387
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 8 (b) 9 (c) 6 (d) 5
  28. 28.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 493 (b) 492 (c) 483 (d) 400
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 58? (a) 17 (b) 5 (c) 16 (d) 15
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 14 (b) 12 (c) 13 (d) 4
  31. 31.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) 144 (b) 51 (c) 48 (d) 16
  32. 32.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 379 (c) 324 (d) 378
  33. 33.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 435 (c) 362 (d) 436
  34. 34.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 14 (b) 3 (c) 13 (d) 12
  36. 36.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 217 (b) 324 (c) 216 (d) 207
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 19 (d) 18
  38. 38.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 43? (a) 4 (b) 5 (c) 2 (d) 3
  40. 40.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) 9 (b) 27 (c) 81 (d) 30

Answer key

  1. 60
  2. 33
  3. 42
  4. 75
  5. 30
  6. 33
  7. 2
  8. 18
  9. 79
  10. 3
  11. 8
  12. 5
  13. 9
  14. 5
  15. 4
  16. 426
  17. 8
  18. 4
  19. 21
  20. 17
  21. 4
  22. 69
  23. 225
  24. 15
  25. 63
  26. 396
  27. 8
  28. 492
  29. 16
  30. 13
  31. 48
  32. 378
  33. 435
  34. 7
  35. 13
  36. 216
  37. 19
  38. 7
  39. 4
  40. 27

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