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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 461 · 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 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) 20 (b) 60 (c) 63 (d) 180
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 2 (b) 4 (c) 3 (d) 5
  3. 3.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  4. 4.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) 152 (c) 134 (d) 144
  5. 5.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
  6. 6.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) 69 (c) 207 (d) 23
  7. 7.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) 109 (c) 118 (d) 110
  8. 8.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) 24 (b) 21 (c) 63 (d) 7
  9. 9.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) 51 (c) 16 (d) 48
  10. 10.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 374 (b) 444 (c) 453 (d) 454
  11. 11.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 6 (b) 17 (c) 16 (d) 18
  13. 13.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 9 (b) 19 (c) 21 (d) 20
  15. 15.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) 213 (d) 220
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 3 (b) 10 (c) 11 (d) 9
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 63? (a) 7 (b) 5 (c) 6 (d) 4
  18. 18.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) 21 (b) 66 (c) 63 (d) 189
  19. 19.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 4 (d) 3
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 7 (b) 6 (c) 5 (d) 4
  21. 21.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 6 (d) 13
  22. 22.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) 15 (b) 5 (c) 18 (d) 45
  23. 23.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 17 (d) 3
  24. 24.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) 198 (d) 66
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 3 (b) 4 (c) 2 (d) 5
  26. 26.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 148 (c) 138 (d) 147
  27. 27.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) 19 (b) 171 (c) 57 (d) 60
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 14 (b) 3 (c) 15 (d) 13
  29. 29.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
  30. 30.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 440 (b) 543 (c) 553 (d) 552
  31. 31.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 123 (c) 114 (d) 124
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 3 (b) 12 (c) 13 (d) 14
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 64? (a) 15 (b) 6 (c) 17 (d) 16
  34. 34.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) 152 (c) 160 (d) 151
  35. 35.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 196 (c) 186 (d) 202
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 17 (b) 15 (c) 6 (d) 16
  37. 37.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  38. 38.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) 117 (c) 42 (d) 39
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 79? (a) 8 (b) 9 (c) 6 (d) 7
  40. 40.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 11 (d) 10

Answer key

  1. 60
  2. 4
  3. 7
  4. 143
  5. 5
  6. 69
  7. 109
  8. 21
  9. 48
  10. 453
  11. 6
  12. 17
  13. 6
  14. 20
  15. 222
  16. 10
  17. 6
  18. 63
  19. 4
  20. 6
  21. 7
  22. 15
  23. 3
  24. 66
  25. 4
  26. 147
  27. 57
  28. 14
  29. 54
  30. 552
  31. 123
  32. 13
  33. 16
  34. 151
  35. 195
  36. 16
  37. 5
  38. 39
  39. 8
  40. 9

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