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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 845 · 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) 10 (b) 5 (c) 7 (d) 6
  2. 2.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) 144 (c) 16 (d) 51
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 14 (b) 15 (c) 16 (d) 4
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 8 (b) 18 (c) 20 (d) 19
  5. 5.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 6 (b) 3 (c) 4 (d) 5
  7. 7.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 74? (a) 7 (b) 16 (c) 17 (d) 18
  9. 9.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) 198 (b) 66 (c) 22 (d) 69
  10. 10.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) 54 (b) 18 (c) 6 (d) 21
  11. 11.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) 27 (c) 24 (d) 72
  12. 12.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 6 (b) 9 (c) 12 (d) 11
  14. 14.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
  15. 15.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 288 (c) 324 (d) 325
  16. 16.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 40 (c) 31 (d) 22
  17. 17.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 600 (c) 609 (d) 478
  18. 18.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 17 (d) 3
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 12 (b) 10 (c) 7 (d) 13
  20. 20.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 368 (b) 445 (c) 444 (d) 435
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 16 (b) 6 (c) 18 (d) 17
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 15 (b) 3 (c) 14 (d) 13
  23. 23.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 198 (c) 180 (d) 189
  24. 24.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 5 (b) 17 (c) 16 (d) 15
  26. 26.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 9 (d) 8
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 6 (b) 16 (c) 18 (d) 17
  28. 28.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 10 (d) 1
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 8 (b) 10 (c) 9 (d) 7
  30. 30.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 229 (b) 224 (c) 219 (d) 228
  31. 31.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 101 (c) 102 (d) 110
  32. 32.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 360 (c) 432 (d) 433
  33. 33.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 202 (c) 206 (d) 201
  34. 34.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) 17 (c) 153 (d) 51
  35. 35.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) 30 (b) 9 (c) 81 (d) 27
  36. 36.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 9 (d) 11
  37. 37.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 318 (c) 370 (d) 369
  38. 38.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 392 (b) 471 (c) 481 (d) 480
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 6 (b) 5 (c) 7 (d) 4
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 87? (a) 16 (b) 17 (c) 14 (d) 8

Answer key

  1. 6
  2. 48
  3. 15
  4. 19
  5. 2
  6. 5
  7. 9
  8. 17
  9. 66
  10. 18
  11. 24
  12. 4
  13. 11
  14. 45
  15. 324
  16. 31
  17. 609
  18. 3
  19. 12
  20. 444
  21. 17
  22. 14
  23. 189
  24. 6
  25. 16
  26. 8
  27. 17
  28. 2
  29. 9
  30. 228
  31. 101
  32. 432
  33. 201
  34. 51
  35. 27
  36. 9
  37. 369
  38. 480
  39. 6
  40. 16

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