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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 329 · 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 4 written when you write all the numbers from 1 to 42? (a) 4 (b) 7 (c) 5 (d) 8
  2. 2.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) 14 (c) 45 (d) 42
  3. 3.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) 39 (b) 36 (c) 12 (d) 108
  4. 4.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
  5. 5.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 16 (b) 6 (c) 18 (d) 17
  7. 7.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
  8. 8.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 37 (b) 38 (c) 28 (d) 46
  9. 9.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) 162 (c) 18 (d) 54
  10. 10.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 169 (b) 160 (c) 170 (d) 178
  11. 11.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 294 (c) 333 (d) 334
  12. 12.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 294 (c) 274 (d) 303
  13. 13.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) 69 (d) 207
  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) 54 (b) 51 (c) 153 (d) 17
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 17 (b) 5 (c) 16 (d) 15
  16. 16.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 3 (b) 4 (c) 5 (d) 6
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 3 (b) 1 (c) 4 (d) 2
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 97? (a) 20 (b) 21 (c) 9 (d) 19
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 4 (b) 6 (c) 3 (d) 5
  21. 21.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
  22. 22.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 496 (c) 402 (d) 495
  23. 23.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 118 (c) 128 (d) 127
  24. 24.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
  25. 25.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 435 (c) 436 (d) 362
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 19 (b) 17 (c) 7 (d) 18
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 18 (b) 20 (c) 8 (d) 19
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 4 (b) 6 (c) 5 (d) 3
  29. 29.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
  30. 30.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) 69 (c) 198 (d) 66
  31. 31.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) 5 (b) 45 (c) 15 (d) 18
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 19 (b) 9 (c) 20 (d) 18
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 4 (b) 6 (c) 7 (d) 5
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 8 (b) 18 (c) 19 (d) 17
  35. 35.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 573 (c) 583 (d) 582
  36. 36.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) 216 (c) 75 (d) 72
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 4 (b) 3 (c) 5 (d) 2
  38. 38.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 532 (b) 531 (c) 522 (d) 426
  39. 39.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
  40. 40.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

Answer key

  1. 7
  2. 42
  3. 36
  4. 5
  5. 3
  6. 17
  7. 3
  8. 37
  9. 54
  10. 169
  11. 333
  12. 303
  13. 69
  14. 51
  15. 16
  16. 6
  17. 5
  18. 3
  19. 20
  20. 5
  21. 4
  22. 495
  23. 127
  24. 9
  25. 435
  26. 18
  27. 19
  28. 5
  29. 19
  30. 66
  31. 15
  32. 19
  33. 6
  34. 18
  35. 582
  36. 72
  37. 4
  38. 531
  39. 195
  40. 21

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