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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 823 · 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 times is the digit 2 written when you write all the numbers from 1 to 86? (a) 20 (b) 8 (c) 18 (d) 19
  2. 2.The numbers 8 to 16 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) 12 (c) 36 (d) 108
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 7 (b) 19 (c) 18 (d) 17
  4. 4.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 352 (c) 420 (d) 421
  5. 5.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) 27 (b) 81 (c) 30 (d) 9
  6. 6.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  7. 7.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 74 (c) 56 (d) 65
  8. 8.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  9. 9.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 496 (c) 402 (d) 486
  10. 10.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 266 (b) 292 (c) 291 (d) 282
  11. 11.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 190 (c) 180 (d) 198
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 65? (a) 5 (b) 7 (c) 4 (d) 6
  13. 13.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
  14. 14.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) 60 (d) 57
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 12 (b) 13 (c) 5 (d) 14
  16. 16.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  17. 17.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) 39 (c) 117 (d) 13
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 94? (a) 18 (b) 9 (c) 20 (d) 19
  19. 19.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 267 (b) 277 (c) 276 (d) 256
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 65? (a) 10 (b) 13 (c) 12 (d) 6
  21. 21.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
  22. 22.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 12 (d) 9
  23. 23.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) 6 (b) 54 (c) 21 (d) 18
  24. 24.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) 126 (b) 45 (c) 42 (d) 14
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 17 (b) 7 (c) 18 (d) 19
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 13 (b) 14 (c) 15 (d) 3
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 17 (b) 15 (c) 16 (d) 5
  28. 28.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) 15 (b) 48 (c) 135 (d) 45
  29. 29.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) 72 (b) 75 (c) 216 (d) 24
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 15 (d) 16
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 1 (b) 3 (c) 2 (d) 4
  32. 32.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  33. 33.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 90? (a) 20 (b) 19 (c) 9 (d) 18
  35. 35.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 4 (d) 2
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 80? (a) 19 (b) 17 (c) 8 (d) 18
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 6 (b) 5 (c) 3 (d) 4
  38. 38.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) 27 (b) 8 (c) 72 (d) 24
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 3 (b) 6 (c) 5 (d) 4
  40. 40.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 313 (c) 312 (d) 303

Answer key

  1. 19
  2. 36
  3. 18
  4. 420
  5. 27
  6. 9
  7. 65
  8. 7
  9. 495
  10. 291
  11. 189
  12. 6
  13. 9
  14. 57
  15. 13
  16. 2
  17. 39
  18. 19
  19. 276
  20. 12
  21. 5
  22. 8
  23. 18
  24. 42
  25. 18
  26. 14
  27. 16
  28. 45
  29. 72
  30. 16
  31. 3
  32. 4
  33. 6
  34. 19
  35. 3
  36. 18
  37. 5
  38. 24
  39. 5
  40. 312

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