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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 320 · 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 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) 12 (c) 36 (d) 108
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 3 (b) 6 (c) 5 (d) 4
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 20 (b) 18 (c) 8 (d) 19
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 75? (a) 14 (b) 13 (c) 11 (d) 7
  5. 5.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 178 (c) 187 (d) 188
  6. 6.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 625 (b) 624 (c) 615 (d) 488
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 61? (a) 4 (b) 5 (c) 7 (d) 6
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 52? (a) 3 (b) 6 (c) 4 (d) 5
  9. 9.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 118 (c) 100 (d) 109
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 16 (b) 14 (c) 15 (d) 4
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 17 (b) 18 (c) 16 (d) 6
  12. 12.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
  13. 13.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 196 (c) 202 (d) 195
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 13 (b) 15 (c) 14 (d) 4
  15. 15.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  16. 16.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) 18 (b) 57 (c) 162 (d) 54
  17. 17.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 8 (d) 10
  18. 18.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 93? (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 72? (a) 7 (b) 18 (c) 17 (d) 19
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 17 (b) 5 (c) 16 (d) 15
  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) 342 (b) 306 (c) 351 (d) 352
  24. 24.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  25. 25.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) 207 (c) 69 (d) 23
  26. 26.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) 21 (b) 18 (c) 54 (d) 6
  27. 27.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) 90 (b) 30 (c) 33 (d) 10
  28. 28.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) 72 (c) 27 (d) 24
  29. 29.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 88 (c) 97 (d) 98
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 96? (a) 19 (b) 20 (c) 9 (d) 21
  31. 31.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 270 (c) 288 (d) 297
  32. 32.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 570 (c) 571 (d) 452
  33. 33.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  34. 34.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 224 (c) 228 (d) 229
  35. 35.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  36. 36.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) 126 (b) 42 (c) 45 (d) 14
  37. 37.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 18 (b) 17 (c) 16 (d) 6
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 4 (b) 14 (c) 13 (d) 15
  40. 40.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5

Answer key

  1. 36
  2. 5
  3. 19
  4. 13
  5. 187
  6. 624
  7. 6
  8. 5
  9. 109
  10. 15
  11. 17
  12. 4
  13. 195
  14. 14
  15. 2
  16. 54
  17. 7
  18. 5
  19. 8
  20. 20
  21. 18
  22. 16
  23. 351
  24. 7
  25. 69
  26. 18
  27. 30
  28. 24
  29. 97
  30. 20
  31. 297
  32. 570
  33. 6
  34. 228
  35. 4
  36. 42
  37. 2
  38. 17
  39. 14
  40. 6

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