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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 557 · 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 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 327 (c) 337 (d) 296
  2. 2.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 601 (b) 472 (c) 591 (d) 600
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 16 (b) 6 (c) 17 (d) 18
  4. 4.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) 14 (b) 42 (c) 45 (d) 126
  5. 5.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  6. 6.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 453 (b) 380 (c) 463 (d) 462
  7. 7.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 16 (b) 17 (c) 5 (d) 15
  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) 511 (b) 501 (c) 412 (d) 510
  10. 10.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
  11. 11.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  13. 13.The numbers 2 to 10 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) 21 (c) 6 (d) 18
  14. 14.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 340 (b) 330 (c) 298 (d) 339
  15. 15.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 267 (b) 276 (c) 256 (d) 277
  16. 16.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 454 (c) 374 (d) 453
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 59? (a) 5 (b) 4 (c) 7 (d) 6
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 7 (b) 19 (c) 18 (d) 17
  19. 19.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 496 (c) 402 (d) 495
  20. 20.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 71 (c) 62 (d) 80
  21. 21.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 338 (c) 399 (d) 400
  22. 22.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) 8 (b) 24 (c) 72 (d) 27
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 4 (b) 16 (c) 14 (d) 15
  24. 24.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 523 (c) 513 (d) 420
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 17 (b) 15 (c) 5 (d) 16
  26. 26.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 93? (a) 9 (b) 18 (c) 19 (d) 20
  29. 29.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4
  30. 30.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) 66 (c) 189 (d) 63
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 11 (b) 4 (c) 12 (d) 10
  32. 32.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
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 56? (a) 3 (b) 5 (c) 4 (d) 6
  34. 34.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) 180 (d) 20
  35. 35.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  36. 36.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 88 (c) 79 (d) 70
  37. 37.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 398 (b) 480 (c) 490 (d) 489
  38. 38.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 63 (c) 54 (d) 72
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 15 (b) 14 (c) 16 (d) 4
  40. 40.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 212 (c) 210 (d) 211

Answer key

  1. 336
  2. 600
  3. 17
  4. 42
  5. 3
  6. 462
  7. 8
  8. 16
  9. 510
  10. 474
  11. 7
  12. 9
  13. 18
  14. 339
  15. 276
  16. 453
  17. 6
  18. 18
  19. 495
  20. 71
  21. 399
  22. 24
  23. 15
  24. 522
  25. 16
  26. 6
  27. 2
  28. 19
  29. 5
  30. 63
  31. 11
  32. 20
  33. 5
  34. 60
  35. 9
  36. 79
  37. 489
  38. 63
  39. 15
  40. 210

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