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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 796 · 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 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) 18 (b) 21 (c) 54 (d) 6
  2. 2.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  3. 3.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 379 (b) 324 (c) 369 (d) 378
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 5 (b) 4 (c) 3 (d) 6
  5. 5.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) 19 (b) 171 (c) 60 (d) 57
  6. 6.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 264 (c) 254 (d) 274
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 19 (b) 18 (c) 17 (d) 8
  8. 8.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  9. 9.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 501 (c) 511 (d) 510
  10. 10.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 23 (c) 69 (d) 207
  11. 11.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 476 (b) 606 (c) 607 (d) 597
  12. 12.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) 10 (b) 33 (c) 90 (d) 30
  13. 13.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) 69 (c) 198 (d) 66
  14. 14.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
  15. 15.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 125 (c) 134 (d) 126
  16. 16.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 21 (c) 24 (d) 7
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 69? (a) 6 (b) 17 (c) 18 (d) 16
  18. 18.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) 615 (d) 625
  19. 19.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) 510 (c) 519 (d) 520
  20. 20.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 44 (c) 26 (d) 35
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 4 (b) 1 (c) 2 (d) 3
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 19 (b) 17 (c) 7 (d) 18
  23. 23.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 493 (c) 400 (d) 492
  24. 24.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  25. 25.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5
  26. 26.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 207 (c) 210 (d) 198
  27. 27.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 121 (c) 130 (d) 122
  28. 28.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 20 (b) 8 (c) 18 (d) 19
  30. 30.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 50 (c) 68 (d) 59
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 2 (b) 4 (c) 5 (d) 3
  32. 32.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) 72 (b) 216 (c) 24 (d) 75
  33. 33.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 562 (c) 561 (d) 446
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 19 (b) 17 (c) 7 (d) 18
  35. 35.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 15 (d) 6
  36. 36.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 14 (b) 13 (c) 3 (d) 15
  38. 38.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 2 (d) 1
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 66? (a) 18 (b) 17 (c) 16 (d) 6
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 16 (b) 4 (c) 14 (d) 15

Answer key

  1. 18
  2. 4
  3. 378
  4. 5
  5. 57
  6. 273
  7. 18
  8. 6
  9. 510
  10. 69
  11. 606
  12. 30
  13. 66
  14. 6
  15. 125
  16. 21
  17. 17
  18. 624
  19. 519
  20. 35
  21. 3
  22. 18
  23. 492
  24. 8
  25. 4
  26. 207
  27. 121
  28. 5
  29. 19
  30. 59
  31. 4
  32. 72
  33. 561
  34. 18
  35. 5
  36. 8
  37. 14
  38. 2
  39. 17
  40. 15

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