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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 528 · 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 7 written when you write all the numbers from 1 to 42? (a) 4 (b) 3 (c) 2 (d) 5
  2. 2.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 367 (b) 316 (c) 357 (d) 366
  3. 3.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 480 (c) 613 (d) 612
  4. 4.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  5. 5.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  6. 6.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) 24 (b) 75 (c) 216 (d) 72
  7. 7.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 146 (c) 137 (d) 138
  8. 8.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 7 (d) 6
  9. 9.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
  10. 10.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) 48 (b) 51 (c) 16 (d) 144
  11. 11.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 444 (c) 549 (d) 559
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 86? (a) 19 (b) 20 (c) 8 (d) 18
  13. 13.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 11 (d) 8
  14. 14.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 202 (c) 206 (d) 201
  15. 15.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 154 (c) 144 (d) 153
  16. 16.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 145 (c) 154 (d) 146
  17. 17.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 4 (b) 2 (c) 5 (d) 3
  18. 18.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (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) 24 (b) 21 (c) 7 (d) 63
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 4 (d) 1
  21. 21.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) 66 (b) 189 (c) 63 (d) 21
  22. 22.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) 42 (c) 14 (d) 45
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 56? (a) 6 (b) 7 (c) 4 (d) 5
  24. 24.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 21 (b) 19 (c) 9 (d) 20
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 1 (b) 3 (c) 4 (d) 2
  27. 27.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) 72 (b) 27 (c) 8 (d) 24
  28. 28.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 71? (a) 8 (b) 6 (c) 5 (d) 7
  30. 30.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  31. 31.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 417 (c) 356 (d) 427
  32. 32.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 202 (c) 196 (d) 195
  33. 33.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
  34. 34.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 5 (b) 2 (c) 4 (d) 3
  36. 36.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 300 (c) 291 (d) 272
  37. 37.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
  38. 38.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) 17 (b) 51 (c) 153 (d) 54
  39. 39.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  40. 40.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) 57 (b) 171 (c) 60 (d) 19

Answer key

  1. 4
  2. 366
  3. 612
  4. 4
  5. 8
  6. 72
  7. 137
  8. 6
  9. 14
  10. 48
  11. 558
  12. 19
  13. 9
  14. 201
  15. 153
  16. 145
  17. 4
  18. 5
  19. 21
  20. 3
  21. 63
  22. 42
  23. 6
  24. 2
  25. 20
  26. 3
  27. 24
  28. 9
  29. 7
  30. 6
  31. 426
  32. 195
  33. 8
  34. 5
  35. 4
  36. 300
  37. 2
  38. 51
  39. 3
  40. 57

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