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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 309 · 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.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) 54 (b) 51 (c) 153 (d) 17
  2. 2.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) 22 (c) 198 (d) 66
  3. 3.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 60 (c) 51 (d) 42
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 14 (b) 15 (c) 4 (d) 16
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 3 (b) 5 (c) 2 (d) 4
  6. 6.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 400 (c) 390 (d) 338
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 58? (a) 16 (b) 15 (c) 17 (d) 5
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 15 (b) 5 (c) 14 (d) 16
  9. 9.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 67? (a) 15 (b) 16 (c) 6 (d) 14
  11. 11.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 9 (d) 7
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 5 (b) 2 (c) 4 (d) 3
  13. 13.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 403 (b) 340 (c) 393 (d) 402
  14. 14.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 11 (d) 8
  15. 15.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  16. 16.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 386 (b) 462 (c) 471 (d) 472
  17. 17.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  18. 18.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  19. 19.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) 412 (c) 510 (d) 501
  20. 20.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) 18 (b) 21 (c) 54 (d) 6
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 4 (b) 3 (c) 2 (d) 1
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
  23. 23.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 3 (d) 2
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 2 (b) 5 (c) 3 (d) 4
  25. 25.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) 72 (c) 27 (d) 24
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 3 (b) 4 (c) 5 (d) 2
  27. 27.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 476 (c) 607 (d) 606
  28. 28.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 18 (b) 9 (c) 20 (d) 19
  30. 30.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 588 (b) 470 (c) 598 (d) 597
  31. 31.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) 51 (d) 144
  32. 32.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) 99 (b) 11 (c) 33 (d) 36
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 4 (b) 5 (c) 2 (d) 3
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 11 (b) 13 (c) 14 (d) 9
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 7 (b) 17 (c) 19 (d) 18
  36. 36.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) 172 (c) 171 (d) 180
  37. 37.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) 72 (b) 75 (c) 24 (d) 216
  38. 38.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 35 (b) 26 (c) 36 (d) 44
  39. 39.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) 45 (b) 135 (c) 15 (d) 48
  40. 40.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 262 (c) 261 (d) 252

Answer key

  1. 51
  2. 66
  3. 51
  4. 15
  5. 4
  6. 399
  7. 16
  8. 15
  9. 8
  10. 15
  11. 8
  12. 4
  13. 402
  14. 9
  15. 5
  16. 471
  17. 3
  18. 3
  19. 510
  20. 18
  21. 3
  22. 2
  23. 2
  24. 4
  25. 24
  26. 4
  27. 606
  28. 9
  29. 19
  30. 597
  31. 48
  32. 33
  33. 4
  34. 13
  35. 18
  36. 171
  37. 72
  38. 35
  39. 45
  40. 261

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