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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 787 · 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 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 196 (c) 187 (d) 178
  2. 2.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) 19 (c) 171 (d) 57
  3. 3.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 418 (c) 350 (d) 417
  4. 4.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 3 (d) 10
  5. 5.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) 54 (c) 21 (d) 6
  6. 6.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) 72 (c) 207 (d) 69
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 7 (b) 19 (c) 17 (d) 18
  8. 8.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) 54 (d) 17
  9. 9.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 4 (d) 6
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 1 (b) 3 (c) 2 (d) 4
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 5 (b) 6 (c) 3 (d) 4
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 73? (a) 9 (b) 7 (c) 11 (d) 12
  13. 13.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
  14. 14.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 17 (d) 3
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 18 (b) 9 (c) 20 (d) 19
  16. 16.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 97? (a) 18 (b) 9 (c) 19 (d) 20
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 53? (a) 15 (b) 17 (c) 5 (d) 16
  19. 19.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  20. 20.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 15 (b) 17 (c) 16 (d) 5
  22. 22.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
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 8 (b) 4 (c) 7 (d) 5
  24. 24.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
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 3 (b) 4 (c) 2 (d) 5
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 5 (b) 4 (c) 2 (d) 3
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 19 (b) 17 (c) 18 (d) 7
  28. 28.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 97? (a) 20 (b) 21 (c) 9 (d) 19
  30. 30.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 471 (c) 386 (d) 462
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 3 (b) 4 (c) 1 (d) 2
  32. 32.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 259 (b) 258 (c) 249 (d) 244
  33. 33.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 205 (c) 208 (d) 204
  34. 34.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) 117 (b) 39 (c) 13 (d) 42
  35. 35.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 15 (b) 14 (c) 4 (d) 16
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 14 (b) 15 (c) 16 (d) 4
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 4 (b) 3 (c) 2 (d) 1
  39. 39.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 547 (b) 537 (c) 546 (d) 436
  40. 40.The numbers 14 to 22 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) 18 (c) 54 (d) 162

Answer key

  1. 187
  2. 57
  3. 417
  4. 4
  5. 18
  6. 69
  7. 18
  8. 51
  9. 5
  10. 3
  11. 5
  12. 11
  13. 7
  14. 3
  15. 19
  16. 6
  17. 19
  18. 16
  19. 2
  20. 7
  21. 16
  22. 15
  23. 7
  24. 48
  25. 4
  26. 4
  27. 18
  28. 4
  29. 20
  30. 471
  31. 3
  32. 258
  33. 204
  34. 39
  35. 2
  36. 15
  37. 15
  38. 3
  39. 546
  40. 54

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