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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 224 · 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 4 written when you write all the numbers from 1 to 99? (a) 20 (b) 21 (c) 9 (d) 19
  2. 2.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 340 (b) 393 (c) 403 (d) 402
  3. 3.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 261 (b) 262 (c) 252 (d) 246
  4. 4.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) 18 (b) 6 (c) 21 (d) 54
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 82? (a) 19 (b) 8 (c) 17 (d) 18
  6. 6.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 126 (c) 117 (d) 108
  7. 7.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) 16 (b) 51 (c) 48 (d) 144
  8. 8.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) 99 (b) 11 (c) 33 (d) 36
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 21 (d) 9
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 4 (b) 15 (c) 13 (d) 14
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 6 (b) 16 (c) 17 (d) 18
  12. 12.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) 72 (b) 23 (c) 207 (d) 69
  13. 13.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) 13 (b) 42 (c) 39 (d) 117
  14. 14.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5
  15. 15.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 186 (c) 177 (d) 168
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 7 (b) 17 (c) 19 (d) 18
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 4 (b) 16 (c) 15 (d) 14
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 8 (b) 18 (c) 20 (d) 19
  19. 19.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) 15 (b) 5 (c) 45 (d) 18
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 83? (a) 8 (b) 20 (c) 19 (d) 18
  21. 21.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  22. 22.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 8 (b) 6 (c) 5 (d) 7
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 3 (b) 5 (c) 2 (d) 4
  25. 25.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  26. 26.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 316 (c) 306 (d) 282
  27. 27.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
  28. 28.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) 33 (b) 30 (c) 10 (d) 90
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 16 (b) 5 (c) 15 (d) 17
  30. 30.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  31. 31.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3
  32. 32.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  33. 33.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) 60 (c) 20 (d) 180
  34. 34.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 104 (c) 94 (d) 103
  35. 35.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
  36. 36.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) 8 (b) 27 (c) 24 (d) 72
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 18 (b) 17 (c) 7 (d) 19
  38. 38.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 471 (c) 481 (d) 392
  39. 39.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 531 (c) 540 (d) 541
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 91? (a) 9 (b) 18 (c) 19 (d) 20

Answer key

  1. 20
  2. 402
  3. 261
  4. 18
  5. 18
  6. 117
  7. 48
  8. 33
  9. 20
  10. 14
  11. 17
  12. 69
  13. 39
  14. 4
  15. 177
  16. 18
  17. 15
  18. 19
  19. 15
  20. 19
  21. 6
  22. 8
  23. 7
  24. 4
  25. 3
  26. 315
  27. 8
  28. 30
  29. 16
  30. 5
  31. 2
  32. 6
  33. 60
  34. 103
  35. 4
  36. 24
  37. 18
  38. 480
  39. 540
  40. 19

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