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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 844 · 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 7? (a) 6 (b) 7 (c) 8 (d) 10
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 3 (b) 13 (c) 15 (d) 14
  3. 3.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) 51 (b) 48 (c) 16 (d) 144
  4. 4.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) 63 (c) 21 (d) 7
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 19 (b) 20 (c) 18 (d) 9
  6. 6.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  7. 7.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  8. 8.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 48 (c) 15 (d) 45
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 6 (b) 18 (c) 16 (d) 17
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 5 (b) 8 (c) 4 (d) 7
  11. 11.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 374 (b) 454 (c) 453 (d) 444
  12. 12.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
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 15 (b) 16 (c) 14 (d) 4
  14. 14.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) 51 (b) 17 (c) 54 (d) 153
  15. 15.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 189 (c) 199 (d) 198
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 16 (b) 18 (c) 17 (d) 6
  17. 17.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 363 (c) 320 (d) 373
  18. 18.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) 30 (b) 90 (c) 33 (d) 10
  19. 19.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) 24 (b) 72 (c) 8 (d) 27
  20. 20.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) 66 (b) 22 (c) 69 (d) 198
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 4 (b) 16 (c) 14 (d) 15
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 2 (b) 3 (c) 1 (d) 4
  23. 23.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) 375 (d) 322
  24. 24.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 375 (c) 385 (d) 384
  25. 25.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) 162 (b) 18 (c) 54 (d) 57
  26. 26.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 414 (c) 415 (d) 405
  27. 27.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) 417 (c) 350 (d) 418
  28. 28.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 232 (c) 222 (d) 226
  29. 29.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 1 (b) 4 (c) 2 (d) 3
  31. 31.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 17 (b) 19 (c) 7 (d) 18
  33. 33.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
  34. 34.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 5 (b) 4 (c) 6 (d) 7
  36. 36.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 15 (b) 14 (c) 13 (d) 3
  38. 38.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 129 (b) 130 (c) 138 (d) 120
  39. 39.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
  40. 40.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 9 (b) 27 (c) 81 (d) 30

Answer key

  1. 7
  2. 14
  3. 48
  4. 21
  5. 19
  6. 3
  7. 2
  8. 45
  9. 17
  10. 7
  11. 453
  12. 18
  13. 15
  14. 51
  15. 198
  16. 17
  17. 372
  18. 30
  19. 24
  20. 66
  21. 15
  22. 3
  23. 375
  24. 384
  25. 54
  26. 414
  27. 417
  28. 231
  29. 6
  30. 3
  31. 6
  32. 18
  33. 7
  34. 9
  35. 6
  36. 2
  37. 14
  38. 129
  39. 20
  40. 27

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