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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 708 · 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 4? (a) 10 (b) 3 (c) 5 (d) 4
  2. 2.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 136 (c) 145 (d) 146
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 1 (b) 2 (c) 4 (d) 3
  4. 4.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 168 (c) 177 (d) 186
  5. 5.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 309 (b) 318 (c) 284 (d) 319
  6. 6.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) 144 (d) 51
  7. 7.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) 201 (c) 210 (d) 211
  8. 8.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 628 (c) 627 (d) 490
  9. 9.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 295 (c) 294 (d) 268
  10. 10.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 180 (c) 172 (d) 171
  11. 11.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 14 (b) 12 (c) 13 (d) 4
  13. 13.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 415 (b) 348 (c) 405 (d) 414
  14. 14.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 631 (c) 630 (d) 621
  15. 15.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 161 (b) 170 (c) 152 (d) 162
  16. 16.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) 90 (b) 33 (c) 10 (d) 30
  17. 17.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 529 (b) 519 (c) 424 (d) 528
  18. 18.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 604 (b) 594 (c) 603 (d) 474
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 8 (b) 9 (c) 6 (d) 7
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 3 (b) 2 (c) 4 (d) 5
  21. 21.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) 594 (d) 595
  22. 22.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
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 19 (b) 17 (c) 18 (d) 7
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 15 (b) 14 (c) 13 (d) 3
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 99? (a) 21 (b) 9 (c) 20 (d) 19
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 20 (b) 9 (c) 19 (d) 21
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 16 (b) 17 (c) 5 (d) 15
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 17 (b) 8 (c) 19 (d) 18
  29. 29.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 12 (d) 7
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 20 (b) 9 (c) 19 (d) 21
  31. 31.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  32. 32.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 445 (b) 444 (c) 368 (d) 435
  33. 33.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) 63 (c) 60 (d) 20
  34. 34.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  35. 35.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 510 (c) 501 (d) 511
  36. 36.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 379 (c) 324 (d) 378
  37. 37.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) 108 (d) 39
  38. 38.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 342 (c) 333 (d) 343
  39. 39.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 4 (d) 2
  40. 40.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) 21 (b) 189 (c) 66 (d) 63

Answer key

  1. 4
  2. 145
  3. 3
  4. 177
  5. 318
  6. 48
  7. 210
  8. 627
  9. 294
  10. 171
  11. 2
  12. 13
  13. 414
  14. 630
  15. 161
  16. 30
  17. 528
  18. 603
  19. 8
  20. 4
  21. 594
  22. 54
  23. 18
  24. 14
  25. 20
  26. 20
  27. 16
  28. 18
  29. 8
  30. 20
  31. 8
  32. 444
  33. 60
  34. 9
  35. 510
  36. 378
  37. 36
  38. 342
  39. 3
  40. 63

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