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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 932 · 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 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) 48 (c) 144 (d) 16
  2. 2.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
  3. 3.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) 24 (b) 75 (c) 216 (d) 72
  4. 4.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 4 (b) 3 (c) 2 (d) 5
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 9 (d) 20
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 70? (a) 7 (b) 18 (c) 16 (d) 17
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 18 (b) 16 (c) 7 (d) 17
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 5 (b) 4 (c) 3 (d) 6
  10. 10.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 70 (c) 78 (d) 69
  11. 11.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) 135 (b) 15 (c) 48 (d) 45
  12. 12.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 6 (d) 15
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 21 (b) 19 (c) 9 (d) 20
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 21 (d) 19
  15. 15.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 52? (a) 3 (b) 4 (c) 6 (d) 5
  17. 17.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) 18 (c) 15 (d) 45
  18. 18.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 450 (c) 558 (d) 568
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 5 (b) 3 (c) 2 (d) 4
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 9 (b) 19 (c) 21 (d) 20
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 16 (b) 14 (c) 15 (d) 4
  22. 22.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 396 (c) 486 (d) 487
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 5 (b) 6 (c) 4 (d) 7
  24. 24.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  25. 25.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 2 (d) 4
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 3 (b) 2 (c) 4 (d) 1
  27. 27.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 91? (a) 9 (b) 19 (c) 18 (d) 20
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 16 (b) 14 (c) 15 (d) 4
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 1 (b) 4 (c) 2 (d) 3
  31. 31.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 14 (b) 16 (c) 5 (d) 15
  33. 33.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 600 (c) 472 (d) 601
  34. 34.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 150 (c) 159 (d) 160
  35. 35.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 402 (c) 495 (d) 496
  36. 36.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 119 (c) 120 (d) 128
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 4 (b) 3 (c) 5 (d) 2
  38. 38.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 307 (c) 297 (d) 306
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 7 (b) 4 (c) 5 (d) 6
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 85? (a) 14 (b) 15 (c) 8 (d) 12

Answer key

  1. 48
  2. 2
  3. 72
  4. 7
  5. 4
  6. 20
  7. 17
  8. 17
  9. 5
  10. 69
  11. 45
  12. 5
  13. 20
  14. 20
  15. 6
  16. 5
  17. 15
  18. 567
  19. 4
  20. 20
  21. 15
  22. 486
  23. 6
  24. 5
  25. 3
  26. 3
  27. 8
  28. 19
  29. 15
  30. 3
  31. 4
  32. 15
  33. 600
  34. 159
  35. 495
  36. 119
  37. 4
  38. 306
  39. 6
  40. 14

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