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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 830 · 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 6? (a) 7 (b) 6 (c) 10 (d) 5
  2. 2.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 65? (a) 18 (b) 16 (c) 17 (d) 6
  4. 4.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  5. 5.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 366 (c) 442 (d) 432
  6. 6.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
  8. 8.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 140 (c) 158 (d) 149
  9. 9.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  10. 10.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) 144 (d) 51
  11. 11.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 555 (b) 565 (c) 448 (d) 564
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  13. 13.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 367 (c) 366 (d) 316
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 18 (b) 19 (c) 20 (d) 8
  15. 15.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) 45 (b) 15 (c) 5 (d) 18
  16. 16.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  17. 17.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 394 (c) 384 (d) 334
  18. 18.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) 57 (b) 171 (c) 60 (d) 19
  19. 19.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 8 (b) 18 (c) 20 (d) 19
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 19 (b) 21 (c) 20 (d) 9
  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) 72 (c) 24 (d) 27
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 9 (b) 21 (c) 19 (d) 20
  24. 24.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) 54 (c) 153 (d) 51
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 99? (a) 9 (b) 20 (c) 19 (d) 21
  26. 26.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 104 (c) 113 (d) 122
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 7 (b) 9 (c) 6 (d) 8
  28. 28.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) 57 (c) 18 (d) 162
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 18 (b) 7 (c) 17 (d) 16
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 2 (b) 4 (c) 1 (d) 3
  31. 31.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 286 (c) 285 (d) 276
  32. 32.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) 66 (d) 21
  33. 33.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) 13 (c) 39 (d) 42
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 3 (b) 5 (c) 4 (d) 2
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 6 (b) 18 (c) 16 (d) 17
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 8 (b) 4 (c) 5 (d) 7
  37. 37.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) 438 (c) 550 (d) 540
  38. 38.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 488 (b) 624 (c) 625 (d) 615
  39. 39.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) 33 (b) 10 (c) 30 (d) 90
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 3 (b) 14 (c) 13 (d) 15

Answer key

  1. 6
  2. 7
  3. 17
  4. 2
  5. 441
  6. 4
  7. 4
  8. 149
  9. 8
  10. 48
  11. 564
  12. 9
  13. 366
  14. 19
  15. 15
  16. 5
  17. 393
  18. 57
  19. 8
  20. 19
  21. 20
  22. 24
  23. 20
  24. 51
  25. 20
  26. 113
  27. 8
  28. 54
  29. 17
  30. 3
  31. 285
  32. 63
  33. 39
  34. 4
  35. 17
  36. 7
  37. 549
  38. 624
  39. 30
  40. 14

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