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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 87 · 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 two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 13 (d) 6
  2. 2.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 284 (b) 318 (c) 309 (d) 319
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 1 (b) 2 (c) 3 (d) 4
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  5. 5.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) 24 (d) 8
  6. 6.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 10 (d) 5
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
  8. 8.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
  9. 9.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 532 (c) 426 (d) 531
  10. 10.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) 21 (c) 54 (d) 18
  11. 11.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 20 (b) 19 (c) 8 (d) 18
  13. 13.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 230 (c) 238 (d) 228
  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) 57 (b) 171 (c) 60 (d) 19
  15. 15.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  16. 16.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 94 (c) 103 (d) 112
  17. 17.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) 54 (c) 162 (d) 18
  18. 18.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 136 (c) 126 (d) 135
  19. 19.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 634 (b) 633 (c) 494 (d) 624
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 18 (d) 19
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 4 (b) 2 (c) 1 (d) 3
  22. 22.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
  23. 23.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) 180 (b) 63 (c) 20 (d) 60
  24. 24.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
  25. 25.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) 69 (b) 72 (c) 23 (d) 207
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 7 (b) 10 (c) 8 (d) 9
  27. 27.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) 90 (b) 33 (c) 10 (d) 30
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 7 (b) 19 (c) 18 (d) 17
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 17 (b) 6 (c) 18 (d) 16
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 21 (b) 19 (c) 20 (d) 9
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 20 (b) 9 (c) 19 (d) 21
  32. 32.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 161 (c) 152 (d) 170
  33. 33.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 11 (d) 8
  34. 34.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) 17 (c) 54 (d) 51
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 21 (b) 20 (c) 19 (d) 9
  36. 36.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) 24 (c) 21 (d) 7
  37. 37.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 382 (c) 465 (d) 456
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 6 (b) 5 (c) 4 (d) 7
  39. 39.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) 16 (c) 51 (d) 144
  40. 40.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 376 (c) 322 (d) 375

Answer key

  1. 7
  2. 318
  3. 3
  4. 5
  5. 24
  6. 6
  7. 4
  8. 8
  9. 531
  10. 18
  11. 5
  12. 19
  13. 237
  14. 57
  15. 4
  16. 103
  17. 54
  18. 135
  19. 633
  20. 19
  21. 3
  22. 9
  23. 60
  24. 3
  25. 69
  26. 9
  27. 30
  28. 18
  29. 17
  30. 20
  31. 20
  32. 161
  33. 9
  34. 51
  35. 20
  36. 21
  37. 465
  38. 6
  39. 48
  40. 375

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