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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 68 · 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 two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  2. 2.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 223 (b) 213 (c) 220 (d) 222
  3. 3.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
  4. 4.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 238 (c) 230 (d) 228
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 65? (a) 6 (b) 18 (c) 16 (d) 17
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 5 (b) 3 (c) 2 (d) 4
  7. 7.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 333 (c) 324 (d) 334
  8. 8.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 9 (d) 7
  9. 9.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 636 (c) 637 (d) 496
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 54? (a) 17 (b) 15 (c) 5 (d) 16
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 45? (a) 5 (b) 4 (c) 3 (d) 2
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 5 (b) 3 (c) 2 (d) 4
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 18 (b) 19 (c) 8 (d) 20
  14. 14.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
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 13 (b) 15 (c) 14 (d) 4
  16. 16.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 520 (c) 519 (d) 510
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 88? (a) 8 (b) 20 (c) 18 (d) 19
  18. 18.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 169 (c) 170 (d) 178
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 65? (a) 16 (b) 18 (c) 6 (d) 17
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 3 (b) 4 (c) 5 (d) 6
  21. 21.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 4 (b) 2 (c) 5 (d) 3
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 13 (b) 15 (c) 3 (d) 14
  24. 24.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
  25. 25.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 625 (b) 615 (c) 488 (d) 624
  26. 26.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 7 (d) 5
  27. 27.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  28. 28.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 39 (b) 30 (c) 40 (d) 48
  29. 29.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 576 (c) 585 (d) 586
  30. 30.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 238 (c) 250 (d) 249
  31. 31.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 9 (c) 27 (d) 30
  32. 32.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 99? (a) 20 (b) 21 (c) 19 (d) 9
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 9 (b) 7 (c) 10 (d) 5
  35. 35.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) 15 (c) 45 (d) 135
  36. 36.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 49 (b) 58 (c) 40 (d) 50
  37. 37.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 571 (c) 452 (d) 561
  38. 38.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) 255 (c) 246 (d) 242
  39. 39.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) 63 (d) 66
  40. 40.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1

Answer key

  1. 5
  2. 222
  3. 48
  4. 237
  5. 17
  6. 4
  7. 333
  8. 8
  9. 636
  10. 16
  11. 4
  12. 4
  13. 19
  14. 15
  15. 14
  16. 519
  17. 19
  18. 169
  19. 17
  20. 5
  21. 4
  22. 4
  23. 14
  24. 6
  25. 624
  26. 6
  27. 9
  28. 39
  29. 585
  30. 249
  31. 27
  32. 3
  33. 20
  34. 9
  35. 45
  36. 49
  37. 570
  38. 255
  39. 63
  40. 2

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