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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 562 · 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 8? (a) 7 (b) 9 (c) 8 (d) 10
  2. 2.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 58? (a) 16 (b) 5 (c) 17 (d) 15
  4. 4.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) 15 (c) 48 (d) 45
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 20 (b) 19 (c) 18 (d) 8
  6. 6.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) 42 (b) 14 (c) 45 (d) 126
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  8. 8.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) 54 (b) 6 (c) 18 (d) 21
  9. 9.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  10. 10.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) 153 (b) 17 (c) 51 (d) 54
  11. 11.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  12. 12.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 118 (c) 128 (d) 127
  13. 13.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 19 (b) 17 (c) 18 (d) 8
  15. 15.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 130 (c) 120 (d) 129
  16. 16.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
  17. 17.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
  18. 18.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) 30 (b) 33 (c) 10 (d) 90
  19. 19.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) 132 (c) 150 (d) 141
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 15 (b) 14 (c) 4 (d) 16
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 3 (b) 15 (c) 13 (d) 14
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 4 (b) 3 (c) 2 (d) 5
  23. 23.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) 254 (c) 274 (d) 264
  24. 24.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) 24 (b) 72 (c) 75 (d) 216
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 6 (b) 5 (c) 7 (d) 8
  26. 26.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 85 (c) 94 (d) 86
  27. 27.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) 30 (b) 81 (c) 9 (d) 27
  28. 28.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 550 (b) 549 (c) 438 (d) 540
  29. 29.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 168 (c) 150 (d) 159
  30. 30.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 189 (c) 180 (d) 190
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 3 (b) 4 (c) 5 (d) 6
  32. 32.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) 207 (b) 23 (c) 69 (d) 72
  33. 33.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
  34. 34.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) 69 (d) 66
  35. 35.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 71 (b) 80 (c) 62 (d) 72
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 6 (b) 5 (c) 7 (d) 8
  37. 37.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) 12 (d) 108
  38. 38.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 331 (c) 321 (d) 292
  39. 39.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) 60 (c) 180 (d) 20
  40. 40.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5

Answer key

  1. 8
  2. 4
  3. 16
  4. 45
  5. 19
  6. 42
  7. 4
  8. 18
  9. 3
  10. 51
  11. 2
  12. 127
  13. 5
  14. 18
  15. 129
  16. 15
  17. 21
  18. 30
  19. 141
  20. 15
  21. 14
  22. 4
  23. 273
  24. 72
  25. 7
  26. 85
  27. 27
  28. 549
  29. 159
  30. 189
  31. 5
  32. 69
  33. 3
  34. 66
  35. 71
  36. 7
  37. 36
  38. 330
  39. 60
  40. 5

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