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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 821 · 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 13? (a) 7 (b) 5 (c) 14 (d) 6
  2. 2.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) 51 (c) 153 (d) 54
  3. 3.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
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
  6. 6.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 4 (b) 1 (c) 2 (d) 3
  8. 8.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) 122 (c) 113 (d) 104
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 15 (b) 5 (c) 16 (d) 14
  10. 10.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 321 (c) 322 (d) 286
  11. 11.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  12. 12.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 126 (c) 135 (d) 136
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 16 (b) 4 (c) 15 (d) 14
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 87? (a) 8 (b) 6 (c) 9 (d) 7
  15. 15.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 11 (d) 8
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 99? (a) 19 (b) 20 (c) 21 (d) 9
  17. 17.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 505 (b) 495 (c) 408 (d) 504
  18. 18.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
  19. 19.The numbers 10 to 18 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) 42 (c) 14 (d) 126
  20. 20.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
  21. 21.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
  22. 22.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) 51 (b) 144 (c) 48 (d) 16
  23. 23.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 352 (c) 351 (d) 342
  24. 24.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 200 (b) 183 (c) 193 (d) 192
  25. 25.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 438 (c) 364 (d) 439
  26. 26.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 334 (c) 294 (d) 333
  27. 27.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 2 (d) 18
  28. 28.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 190 (c) 181 (d) 182
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 14 (b) 4 (c) 15 (d) 16
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 44? (a) 2 (b) 5 (c) 4 (d) 3
  31. 31.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
  32. 32.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) 22 (b) 66 (c) 69 (d) 198
  33. 33.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) 472 (c) 462 (d) 471
  34. 34.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) 18 (c) 162 (d) 57
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 5 (b) 6 (c) 7 (d) 4
  36. 36.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 429 (c) 358 (d) 420
  37. 37.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 3 (b) 13 (c) 15 (d) 14
  39. 39.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 5 (b) 6 (c) 7 (d) 4

Answer key

  1. 6
  2. 51
  3. 45
  4. 5
  5. 6
  6. 7
  7. 3
  8. 113
  9. 15
  10. 321
  11. 3
  12. 135
  13. 15
  14. 8
  15. 9
  16. 20
  17. 504
  18. 9
  19. 42
  20. 39
  21. 7
  22. 48
  23. 351
  24. 192
  25. 438
  26. 333
  27. 2
  28. 181
  29. 15
  30. 4
  31. 8
  32. 66
  33. 471
  34. 54
  35. 6
  36. 429
  37. 4
  38. 14
  39. 2
  40. 6

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