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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 180 · 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 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 270 (c) 297 (d) 288
  2. 2.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 254 (c) 264 (d) 274
  3. 3.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) 27 (b) 8 (c) 72 (d) 24
  4. 4.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) 10 (c) 33 (d) 90
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 20 (b) 19 (c) 21 (d) 9
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 2 (b) 4 (c) 3 (d) 1
  7. 7.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
  8. 8.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  9. 9.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 501 (c) 412 (d) 511
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 92? (a) 20 (b) 9 (c) 18 (d) 19
  11. 11.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 154 (c) 164 (d) 163
  12. 12.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 577 (b) 567 (c) 456 (d) 576
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 21 (d) 19
  14. 14.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) 30 (c) 27 (d) 81
  15. 15.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 206 (b) 192 (c) 202 (d) 201
  16. 16.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
  17. 17.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) 57 (d) 171
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 17 (b) 7 (c) 16 (d) 18
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 4 (b) 5 (c) 6 (d) 3
  20. 20.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  21. 21.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 11 (b) 99 (c) 36 (d) 33
  22. 22.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 625 (b) 615 (c) 488 (d) 624
  23. 23.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 104 (c) 95 (d) 96
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 90? (a) 18 (b) 20 (c) 19 (d) 9
  25. 25.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 6 (d) 4
  26. 26.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 101 (b) 110 (c) 102 (d) 92
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 12 (b) 8 (c) 10 (d) 13
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 18 (b) 7 (c) 16 (d) 17
  29. 29.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) 16 (b) 51 (c) 144 (d) 48
  30. 30.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  31. 31.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 405 (c) 396 (d) 406
  32. 32.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 168 (c) 159 (d) 160
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 20 (b) 9 (c) 18 (d) 19
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 2 (b) 4 (c) 5 (d) 3
  35. 35.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) 69 (b) 22 (c) 66 (d) 198
  36. 36.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) 153 (c) 51 (d) 17
  37. 37.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 526 (b) 422 (c) 516 (d) 525
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 4 (b) 2 (c) 3 (d) 5
  39. 39.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 116 (c) 106 (d) 115
  40. 40.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1

Answer key

  1. 297
  2. 273
  3. 24
  4. 30
  5. 20
  6. 3
  7. 6
  8. 4
  9. 510
  10. 19
  11. 163
  12. 576
  13. 20
  14. 27
  15. 201
  16. 9
  17. 57
  18. 17
  19. 5
  20. 3
  21. 33
  22. 624
  23. 95
  24. 19
  25. 5
  26. 101
  27. 12
  28. 17
  29. 48
  30. 7
  31. 405
  32. 159
  33. 19
  34. 4
  35. 66
  36. 51
  37. 525
  38. 4
  39. 115
  40. 2

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