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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 141 · 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 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 480 (c) 613 (d) 612
  2. 2.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 549 (b) 550 (c) 540 (d) 438
  3. 3.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 266 (c) 292 (d) 282
  4. 4.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 20 (b) 18 (c) 9 (d) 19
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 14 (b) 15 (c) 13 (d) 4
  7. 7.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 42 (c) 13 (d) 39
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 6 (b) 4 (c) 7 (d) 5
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 63? (a) 11 (b) 10 (c) 8 (d) 6
  10. 10.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 151 (b) 142 (c) 160 (d) 152
  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) 24 (b) 21 (c) 7 (d) 63
  12. 12.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
  13. 13.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 385 (b) 384 (c) 375 (d) 328
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 60? (a) 16 (b) 17 (c) 15 (d) 6
  15. 15.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
  16. 16.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 9 (d) 12
  17. 17.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  18. 18.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  19. 19.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 243 (b) 351 (c) 234 (d) 244
  20. 20.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) 16 (b) 144 (c) 48 (d) 51
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 94? (a) 9 (b) 20 (c) 18 (d) 19
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 5 (b) 17 (c) 15 (d) 16
  23. 23.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 579 (c) 570 (d) 580
  24. 24.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) 36 (b) 11 (c) 99 (d) 33
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 17 (b) 15 (c) 16 (d) 6
  26. 26.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 41 (c) 32 (d) 50
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 79? (a) 19 (b) 17 (c) 7 (d) 18
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 4 (b) 3 (c) 2 (d) 1
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 13 (b) 15 (c) 3 (d) 14
  30. 30.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 67? (a) 6 (b) 15 (c) 16 (d) 14
  32. 32.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 607 (b) 597 (c) 476 (d) 606
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 68? (a) 6 (b) 5 (c) 8 (d) 7
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 18 (b) 19 (c) 7 (d) 17
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 14 (b) 12 (c) 3 (d) 13
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 18 (b) 16 (c) 6 (d) 17
  37. 37.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) 69 (b) 66 (c) 198 (d) 22
  38. 38.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) 319 (c) 318 (d) 284
  39. 39.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) 60 (b) 57 (c) 19 (d) 171
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 51? (a) 16 (b) 5 (c) 14 (d) 15

Answer key

  1. 612
  2. 549
  3. 291
  4. 6
  5. 19
  6. 14
  7. 39
  8. 6
  9. 10
  10. 151
  11. 21
  12. 30
  13. 384
  14. 16
  15. 3
  16. 8
  17. 2
  18. 3
  19. 243
  20. 48
  21. 19
  22. 16
  23. 579
  24. 33
  25. 16
  26. 41
  27. 18
  28. 3
  29. 14
  30. 9
  31. 15
  32. 606
  33. 7
  34. 18
  35. 13
  36. 17
  37. 66
  38. 318
  39. 57
  40. 15

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