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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 556 · 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 2 written when you write all the numbers from 1 to 73? (a) 19 (b) 18 (c) 7 (d) 17
  2. 2.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  3. 3.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 8 (d) 11
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 17 (b) 15 (c) 9 (d) 18
  5. 5.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 250 (c) 267 (d) 268
  6. 6.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
  7. 7.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 415 (c) 414 (d) 405
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 18 (b) 7 (c) 17 (d) 19
  9. 9.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 14 (b) 3 (c) 13 (d) 15
  11. 11.The numbers 11 to 19 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) 45 (c) 15 (d) 135
  12. 12.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 32 (c) 22 (d) 31
  13. 13.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) 72 (c) 8 (d) 24
  14. 14.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 460 (c) 459 (d) 450
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 2 (b) 3 (c) 1 (d) 4
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 3 (b) 2 (c) 4 (d) 5
  17. 17.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 135 (b) 144 (c) 126 (d) 136
  18. 18.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  19. 19.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  20. 20.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 350 (b) 417 (c) 418 (d) 408
  21. 21.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) 15 (c) 45 (d) 18
  22. 22.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 264 (c) 273 (d) 254
  23. 23.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 630 (b) 492 (c) 621 (d) 631
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 6 (b) 5 (c) 4 (d) 7
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 6 (b) 8 (c) 5 (d) 7
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 16 (b) 4 (c) 14 (d) 15
  27. 27.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 640 (c) 639 (d) 630
  28. 28.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
  29. 29.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 2 (b) 3 (c) 1 (d) 4
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 85? (a) 15 (b) 8 (c) 12 (d) 14
  32. 32.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) 333 (c) 294 (d) 334
  33. 33.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 351 (c) 243 (d) 234
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 12 (b) 14 (c) 3 (d) 13
  35. 35.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 7 (d) 6
  36. 36.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 471 (b) 480 (c) 481 (d) 392
  37. 37.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
  38. 38.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
  39. 39.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 474 (c) 475 (d) 388
  40. 40.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 154 (c) 136 (d) 145

Answer key

  1. 18
  2. 2
  3. 9
  4. 17
  5. 267
  6. 66
  7. 414
  8. 18
  9. 3
  10. 14
  11. 45
  12. 31
  13. 24
  14. 459
  15. 3
  16. 4
  17. 135
  18. 2
  19. 6
  20. 417
  21. 15
  22. 273
  23. 630
  24. 6
  25. 7
  26. 15
  27. 639
  28. 7
  29. 5
  30. 3
  31. 14
  32. 333
  33. 243
  34. 13
  35. 7
  36. 480
  37. 63
  38. 9
  39. 474
  40. 145

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