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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 183 · 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 12? (a) 13 (b) 7 (c) 8 (d) 6
  2. 2.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 630 (b) 640 (c) 498 (d) 639
  3. 3.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 434 (b) 544 (c) 534 (d) 543
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 74? (a) 5 (b) 8 (c) 6 (d) 7
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 8 (b) 7 (c) 9 (d) 10
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 17 (b) 8 (c) 18 (d) 19
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 2 (b) 1 (c) 3 (d) 4
  8. 8.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) 7 (b) 24 (c) 21 (d) 63
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 9 (b) 18 (c) 19 (d) 20
  10. 10.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 140 (c) 130 (d) 139
  11. 11.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 69 (b) 60 (c) 78 (d) 70
  12. 12.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) 45 (c) 48 (d) 15
  13. 13.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 11 (b) 99 (c) 36 (d) 33
  14. 14.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 17 (d) 3
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 19 (b) 18 (c) 7 (d) 17
  16. 16.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 67 (c) 58 (d) 76
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 84? (a) 18 (b) 8 (c) 17 (d) 19
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 64? (a) 6 (b) 15 (c) 17 (d) 16
  19. 19.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 95 (b) 104 (c) 86 (d) 96
  20. 20.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 492 (c) 630 (d) 631
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 73? (a) 16 (b) 17 (c) 18 (d) 7
  22. 22.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  23. 23.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) 625 (c) 624 (d) 615
  24. 24.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 600 (b) 610 (c) 478 (d) 609
  25. 25.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 97? (a) 20 (b) 19 (c) 9 (d) 18
  27. 27.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) 198 (c) 66 (d) 69
  28. 28.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 3 (d) 1
  29. 29.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 2 (d) 4
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 19 (b) 17 (c) 18 (d) 7
  31. 31.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 225 (b) 234 (c) 235 (d) 228
  32. 32.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) 90 (d) 30
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 60? (a) 15 (b) 16 (c) 6 (d) 17
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 99? (a) 19 (b) 9 (c) 20 (d) 21
  35. 35.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) 18 (b) 15 (c) 5 (d) 45
  36. 36.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
  37. 37.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 218 (b) 210 (c) 219 (d) 220
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 5 (b) 15 (c) 16 (d) 17
  39. 39.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 456 (c) 577 (d) 567
  40. 40.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 108 (c) 36 (d) 12

Answer key

  1. 7
  2. 639
  3. 543
  4. 7
  5. 9
  6. 18
  7. 3
  8. 21
  9. 19
  10. 139
  11. 69
  12. 45
  13. 33
  14. 3
  15. 18
  16. 67
  17. 18
  18. 16
  19. 95
  20. 630
  21. 17
  22. 9
  23. 624
  24. 609
  25. 4
  26. 19
  27. 66
  28. 2
  29. 3
  30. 18
  31. 234
  32. 30
  33. 16
  34. 20
  35. 15
  36. 324
  37. 219
  38. 16
  39. 576
  40. 36

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