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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 501 · 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 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 340 (c) 402 (d) 403
  2. 2.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 5 (d) 16
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 9 (b) 10 (c) 11 (d) 3
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 8 (d) 19
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 51? (a) 16 (b) 15 (c) 5 (d) 14
  6. 6.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) 510 (d) 412
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  8. 8.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) 189 (b) 63 (c) 21 (d) 66
  9. 9.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 19 (d) 18
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 4 (b) 3 (c) 1 (d) 2
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 64? (a) 16 (b) 18 (c) 6 (d) 17
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 67? (a) 16 (b) 15 (c) 14 (d) 6
  15. 15.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 90 (c) 108 (d) 99
  16. 16.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) 198 (c) 66 (d) 22
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 16 (b) 17 (c) 6 (d) 18
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 18 (b) 17 (c) 16 (d) 6
  19. 19.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 306 (c) 315 (d) 282
  20. 20.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) 108 (b) 36 (c) 39 (d) 12
  21. 21.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 75 (b) 24 (c) 216 (d) 72
  22. 22.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 373 (b) 363 (c) 372 (d) 320
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 9 (b) 20 (c) 19 (d) 18
  24. 24.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  25. 25.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  26. 26.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 153 (c) 54 (d) 51
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 14 (b) 4 (c) 16 (d) 15
  28. 28.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 429 (c) 430 (d) 420
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 7 (b) 5 (c) 4 (d) 6
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 88? (a) 8 (b) 19 (c) 17 (d) 18
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 16 (b) 14 (c) 4 (d) 15
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 7 (b) 8 (c) 6 (d) 5
  33. 33.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 246 (c) 242 (d) 255
  34. 34.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 1 (d) 4
  36. 36.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 65? (a) 16 (b) 6 (c) 17 (d) 18
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 18 (b) 19 (c) 20 (d) 9
  39. 39.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) 54 (b) 162 (c) 57 (d) 18
  40. 40.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) 319 (d) 284

Answer key

  1. 402
  2. 4
  3. 10
  4. 19
  5. 15
  6. 510
  7. 4
  8. 63
  9. 3
  10. 3
  11. 19
  12. 3
  13. 17
  14. 15
  15. 99
  16. 66
  17. 17
  18. 17
  19. 315
  20. 36
  21. 72
  22. 372
  23. 19
  24. 6
  25. 7
  26. 51
  27. 15
  28. 429
  29. 6
  30. 18
  31. 15
  32. 7
  33. 255
  34. 2
  35. 3
  36. 5
  37. 17
  38. 19
  39. 54
  40. 318

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