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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 793 · 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 times is the digit 2 written when you write all the numbers from 1 to 39? (a) 13 (b) 3 (c) 15 (d) 14
  2. 2.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  3. 3.The numbers 16 to 24 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) 20 (c) 60 (d) 180
  4. 4.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 115 (c) 116 (d) 106
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 7 (b) 5 (c) 4 (d) 6
  6. 6.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 6 (b) 7 (c) 5 (d) 4
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 8 (b) 19 (c) 20 (d) 18
  9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 3 (b) 4 (c) 2 (d) 1
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 45? (a) 6 (b) 4 (c) 5 (d) 3
  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) 72 (b) 8 (c) 27 (d) 24
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 64? (a) 17 (b) 6 (c) 18 (d) 16
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 6 (b) 7 (c) 8 (d) 5
  14. 14.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) 30 (d) 90
  15. 15.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 99 (c) 108 (d) 90
  16. 16.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) 36 (b) 39 (c) 108 (d) 12
  17. 17.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 94 (c) 93 (d) 84
  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) 624 (b) 488 (c) 615 (d) 625
  19. 19.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) 144 (b) 48 (c) 16 (d) 51
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 19 (b) 9 (c) 21 (d) 20
  21. 21.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) 81 (b) 9 (c) 30 (d) 27
  22. 22.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 7 (b) 18 (c) 16 (d) 17
  24. 24.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 340 (c) 330 (d) 298
  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) 23 (b) 72 (c) 69 (d) 207
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 62? (a) 5 (b) 4 (c) 6 (d) 7
  27. 27.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 285 (c) 286 (d) 262
  28. 28.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 39 (c) 117 (d) 13
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 49? (a) 5 (b) 6 (c) 3 (d) 4
  30. 30.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 26 (c) 36 (d) 35
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 4 (b) 7 (c) 5 (d) 6
  32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 4 (b) 1 (c) 3 (d) 2
  33. 33.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 140 (c) 131 (d) 132
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 20 (b) 19 (c) 18 (d) 8
  35. 35.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  36. 36.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) 45 (c) 18 (d) 15
  37. 37.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 154 (c) 144 (d) 153
  38. 38.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 252 (c) 261 (d) 271
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 18 (b) 19 (c) 7 (d) 17
  40. 40.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

Answer key

  1. 14
  2. 3
  3. 60
  4. 115
  5. 6
  6. 2
  7. 6
  8. 19
  9. 3
  10. 5
  11. 24
  12. 17
  13. 7
  14. 30
  15. 99
  16. 36
  17. 93
  18. 624
  19. 48
  20. 20
  21. 27
  22. 8
  23. 17
  24. 339
  25. 69
  26. 6
  27. 285
  28. 39
  29. 5
  30. 35
  31. 6
  32. 3
  33. 131
  34. 19
  35. 5
  36. 15
  37. 153
  38. 270
  39. 18
  40. 219

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