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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 35 · 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 15? (a) 5 (b) 16 (c) 3 (d) 4
  2. 2.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) 13 (b) 42 (c) 117 (d) 39
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 13 (b) 15 (c) 14 (d) 3
  4. 4.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 243 (c) 240 (d) 253
  5. 5.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 385 (c) 375 (d) 384
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 19 (b) 20 (c) 9 (d) 18
  7. 7.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) 66 (b) 189 (c) 63 (d) 21
  8. 8.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 7 (d) 8
  9. 9.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
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 15 (b) 5 (c) 16 (d) 17
  11. 11.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) 69 (c) 66 (d) 198
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 2 (b) 4 (c) 1 (d) 3
  13. 13.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  14. 14.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) 216 (b) 24 (c) 72 (d) 75
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 16 (b) 17 (c) 15 (d) 5
  16. 16.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) 48 (b) 45 (c) 135 (d) 15
  17. 17.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 151 (c) 160 (d) 152
  18. 18.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 5 (b) 2 (c) 4 (d) 3
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 7 (b) 17 (c) 16 (d) 18
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 15 (b) 16 (c) 14 (d) 4
  22. 22.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 19 (c) 57 (d) 171
  23. 23.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) 180 (d) 60
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 16 (d) 15
  25. 25.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 248 (c) 265 (d) 264
  26. 26.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) 27 (b) 30 (c) 9 (d) 81
  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) 10 (c) 30 (d) 33
  28. 28.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 278 (b) 310 (c) 309 (d) 300
  29. 29.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 5 (b) 12 (c) 13 (d) 14
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 5 (b) 2 (c) 3 (d) 4
  32. 32.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 15 (b) 14 (c) 13 (d) 4
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 19 (b) 18 (c) 8 (d) 20
  35. 35.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
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 5 (b) 16 (c) 15 (d) 17
  37. 37.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
  38. 38.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 45 (c) 54 (d) 36
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 2 (b) 4 (c) 1 (d) 3
  40. 40.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 118 (c) 110 (d) 109

Answer key

  1. 4
  2. 39
  3. 14
  4. 252
  5. 384
  6. 19
  7. 63
  8. 8
  9. 18
  10. 16
  11. 66
  12. 3
  13. 5
  14. 72
  15. 16
  16. 45
  17. 151
  18. 7
  19. 4
  20. 17
  21. 15
  22. 57
  23. 60
  24. 16
  25. 264
  26. 27
  27. 30
  28. 309
  29. 7
  30. 13
  31. 4
  32. 2
  33. 14
  34. 19
  35. 48
  36. 16
  37. 9
  38. 45
  39. 3
  40. 109

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