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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 425 · 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 4 written when you write all the numbers from 1 to 43? (a) 6 (b) 9 (c) 8 (d) 4
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 15 (b) 16 (c) 5 (d) 17
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 18 (d) 8
  4. 4.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 141 (c) 132 (d) 150
  5. 5.The numbers 17 to 25 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) 189 (c) 66 (d) 21
  6. 6.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 18 (b) 17 (c) 7 (d) 16
  8. 8.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
  9. 9.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 11 (d) 10
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 93? (a) 9 (b) 18 (c) 19 (d) 20
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 8 (b) 19 (c) 17 (d) 18
  12. 12.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 143 (b) 144 (c) 134 (d) 152
  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) 33 (b) 11 (c) 36 (d) 99
  14. 14.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) 69 (b) 22 (c) 66 (d) 198
  15. 15.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) 51 (b) 17 (c) 153 (d) 54
  16. 16.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 634 (c) 494 (d) 633
  17. 17.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 69 (c) 60 (d) 70
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 4 (b) 2 (c) 5 (d) 3
  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) 16 (b) 48 (c) 51 (d) 144
  20. 20.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) 24 (d) 27
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 16 (b) 4 (c) 14 (d) 15
  22. 22.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 390 (c) 332 (d) 391
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 37? (a) 2 (b) 4 (c) 3 (d) 1
  24. 24.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) 45 (c) 42 (d) 14
  25. 25.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 223 (c) 220 (d) 213
  26. 26.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 184 (c) 176 (d) 175
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 63? (a) 5 (b) 4 (c) 7 (d) 6
  29. 29.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 80 (c) 70 (d) 79
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 4 (b) 1 (c) 2 (d) 3
  31. 31.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) 609 (c) 478 (d) 610
  32. 32.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 356 (c) 417 (d) 427
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 88? (a) 19 (b) 18 (c) 17 (d) 8
  34. 34.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 138 (c) 120 (d) 129
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 50? (a) 4 (b) 3 (c) 6 (d) 5
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 5 (b) 4 (c) 2 (d) 3
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 92? (a) 21 (b) 9 (c) 20 (d) 19
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 3 (b) 6 (c) 4 (d) 5
  39. 39.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 127 (b) 118 (c) 136 (d) 128
  40. 40.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) 54 (b) 18 (c) 162 (d) 57

Answer key

  1. 8
  2. 16
  3. 18
  4. 141
  5. 63
  6. 8
  7. 17
  8. 7
  9. 9
  10. 19
  11. 18
  12. 143
  13. 33
  14. 66
  15. 51
  16. 633
  17. 69
  18. 4
  19. 48
  20. 24
  21. 15
  22. 390
  23. 3
  24. 42
  25. 222
  26. 175
  27. 2
  28. 6
  29. 79
  30. 3
  31. 609
  32. 426
  33. 18
  34. 129
  35. 5
  36. 4
  37. 20
  38. 5
  39. 127
  40. 54

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