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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 142 · 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 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 356 (b) 417 (c) 427 (d) 426
  2. 2.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) 36 (b) 12 (c) 39 (d) 108
  3. 3.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 456 (c) 466 (d) 465
  4. 4.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 434 (b) 544 (c) 543 (d) 534
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 17 (b) 16 (c) 18 (d) 6
  6. 6.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 133 (b) 142 (c) 134 (d) 124
  7. 7.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 15 (b) 5 (c) 14 (d) 16
  9. 9.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) 72 (b) 69 (c) 207 (d) 23
  10. 10.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  11. 11.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
  12. 12.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 132 (c) 142 (d) 141
  13. 13.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 149 (c) 150 (d) 158
  14. 14.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 8 (b) 19 (c) 18 (d) 20
  16. 16.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 58? (a) 15 (b) 16 (c) 17 (d) 5
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 9 (b) 19 (c) 21 (d) 20
  19. 19.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
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 12 (b) 3 (c) 10 (d) 11
  21. 21.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  22. 22.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  23. 23.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 456 (c) 457 (d) 447
  24. 24.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 168 (c) 150 (d) 159
  25. 25.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 8 (d) 13
  26. 26.The numbers 17 to 25 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) 21 (c) 189 (d) 63
  27. 27.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) 36 (c) 99 (d) 33
  28. 28.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
  29. 29.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 379 (c) 369 (d) 378
  30. 30.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 465 (c) 474 (d) 475
  31. 31.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) 81 (d) 27
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 46? (a) 11 (b) 4 (c) 12 (d) 13
  33. 33.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 528 (b) 424 (c) 529 (d) 519
  34. 34.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 212 (b) 210 (c) 211 (d) 201
  35. 35.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 564 (b) 555 (c) 448 (d) 565
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 3 (b) 2 (c) 4 (d) 5
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 5 (b) 4 (c) 6 (d) 3
  38. 38.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 324 (c) 334 (d) 333
  39. 39.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) 60 (b) 63 (c) 20 (d) 180
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 16 (b) 7 (c) 18 (d) 17

Answer key

  1. 426
  2. 36
  3. 465
  4. 543
  5. 17
  6. 133
  7. 5
  8. 15
  9. 69
  10. 5
  11. 21
  12. 141
  13. 149
  14. 2
  15. 19
  16. 8
  17. 16
  18. 20
  19. 48
  20. 11
  21. 9
  22. 3
  23. 456
  24. 159
  25. 7
  26. 63
  27. 33
  28. 6
  29. 378
  30. 474
  31. 27
  32. 12
  33. 528
  34. 210
  35. 564
  36. 4
  37. 5
  38. 333
  39. 60
  40. 17

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