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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 196 · 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 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 468 (c) 595 (d) 594
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 4 (b) 16 (c) 15 (d) 14
  3. 3.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) 72 (c) 75 (d) 216
  4. 4.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 270 (c) 258 (d) 280
  5. 5.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 15 (b) 16 (c) 6 (d) 17
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 68? (a) 5 (b) 6 (c) 7 (d) 4
  8. 8.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  9. 9.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  10. 10.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) 54 (b) 162 (c) 18 (d) 57
  11. 11.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 183 (b) 184 (c) 174 (d) 192
  12. 12.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) 20 (c) 63 (d) 60
  13. 13.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 217 (c) 216 (d) 324
  14. 14.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 544 (b) 534 (c) 434 (d) 543
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 19 (b) 8 (c) 17 (d) 18
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 6 (b) 16 (c) 18 (d) 17
  17. 17.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  18. 18.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) 8 (c) 27 (d) 72
  19. 19.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  20. 20.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 459 (c) 468 (d) 469
  21. 21.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) 202 (c) 201 (d) 192
  22. 22.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 108 (c) 118 (d) 117
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 7 (b) 17 (c) 19 (d) 18
  24. 24.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) 54 (d) 153
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 80? (a) 19 (b) 18 (c) 17 (d) 8
  26. 26.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  27. 27.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) 19 (b) 171 (c) 57 (d) 60
  28. 28.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 3 (b) 5 (c) 2 (d) 4
  30. 30.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 387 (c) 388 (d) 378
  31. 31.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) 160 (d) 159
  32. 32.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  33. 33.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) 612 (c) 480 (d) 613
  34. 34.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) 45 (c) 14 (d) 42
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 19 (b) 18 (c) 20 (d) 8
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 19 (b) 7 (c) 17 (d) 18
  37. 37.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 92 (c) 91 (d) 100
  38. 38.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 127 (b) 136 (c) 118 (d) 128
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 19 (b) 20 (c) 8 (d) 18
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 14 (b) 5 (c) 16 (d) 15

Answer key

  1. 594
  2. 15
  3. 72
  4. 279
  5. 4
  6. 16
  7. 6
  8. 7
  9. 3
  10. 54
  11. 183
  12. 60
  13. 216
  14. 543
  15. 18
  16. 17
  17. 4
  18. 24
  19. 5
  20. 468
  21. 201
  22. 117
  23. 18
  24. 51
  25. 18
  26. 7
  27. 57
  28. 8
  29. 4
  30. 387
  31. 159
  32. 5
  33. 612
  34. 42
  35. 19
  36. 18
  37. 91
  38. 127
  39. 19
  40. 15

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