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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 351 · 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 75? (a) 17 (b) 18 (c) 19 (d) 7
  2. 2.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 288 (c) 324 (d) 325
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 65? (a) 16 (b) 18 (c) 6 (d) 17
  5. 5.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) 42 (b) 14 (c) 126 (d) 45
  6. 6.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 99 (b) 100 (c) 90 (d) 108
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 18 (b) 7 (c) 19 (d) 17
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 5 (b) 4 (c) 3 (d) 2
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 86? (a) 8 (b) 19 (c) 20 (d) 18
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 3 (b) 2 (c) 1 (d) 4
  11. 11.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 12 (d) 9
  12. 12.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 79? (a) 7 (b) 17 (c) 18 (d) 19
  14. 14.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 318 (c) 369 (d) 370
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 20 (b) 19 (c) 21 (d) 9
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 17 (b) 16 (c) 15 (d) 5
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 16 (b) 15 (c) 14 (d) 5
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 3 (b) 13 (c) 15 (d) 14
  19. 19.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) 63 (b) 66 (c) 189 (d) 21
  20. 20.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) 108 (b) 12 (c) 39 (d) 36
  21. 21.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
  22. 22.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) 30 (c) 33 (d) 90
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 56? (a) 7 (b) 4 (c) 5 (d) 6
  24. 24.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) 72 (d) 24
  25. 25.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 198 (c) 69 (d) 66
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 20 (b) 18 (c) 19 (d) 8
  27. 27.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 504 (c) 414 (d) 514
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 4 (b) 3 (c) 2 (d) 1
  29. 29.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  30. 30.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) 60 (b) 171 (c) 57 (d) 19
  31. 31.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) 36 (b) 99 (c) 33 (d) 11
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 70? (a) 8 (b) 5 (c) 6 (d) 7
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 77? (a) 19 (b) 17 (c) 7 (d) 18
  34. 34.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) 42 (c) 34 (d) 33
  35. 35.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) 216 (b) 72 (c) 24 (d) 75
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 16 (b) 6 (c) 17 (d) 18
  37. 37.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
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 8 (b) 18 (c) 19 (d) 20
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 3 (d) 2
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 12 (b) 9 (c) 11 (d) 6

Answer key

  1. 18
  2. 324
  3. 5
  4. 17
  5. 42
  6. 99
  7. 18
  8. 4
  9. 19
  10. 3
  11. 8
  12. 2
  13. 18
  14. 369
  15. 20
  16. 16
  17. 15
  18. 14
  19. 63
  20. 36
  21. 2
  22. 30
  23. 6
  24. 24
  25. 66
  26. 19
  27. 513
  28. 3
  29. 5
  30. 57
  31. 33
  32. 7
  33. 18
  34. 33
  35. 72
  36. 17
  37. 21
  38. 19
  39. 3
  40. 11

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