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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 985 · 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 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) 18 (c) 5 (d) 45
  2. 2.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  3. 3.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) 8 (b) 72 (c) 27 (d) 24
  4. 4.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 12 (d) 9
  5. 5.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 312 (c) 351 (d) 361
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 19 (b) 7 (c) 18 (d) 17
  7. 7.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) 45 (b) 48 (c) 135 (d) 15
  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) 21 (c) 18 (d) 6
  9. 9.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 102 (c) 111 (d) 112
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 21 (b) 19 (c) 9 (d) 20
  11. 11.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) 117 (c) 39 (d) 13
  12. 12.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  13. 13.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) 66 (b) 69 (c) 198 (d) 22
  14. 14.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 192 (c) 183 (d) 174
  15. 15.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 11 (d) 8
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 9 (b) 19 (c) 20 (d) 18
  17. 17.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 283 (b) 260 (c) 282 (d) 273
  18. 18.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 7 (d) 8
  19. 19.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) 72 (c) 69 (d) 23
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 3 (b) 4 (c) 2 (d) 1
  21. 21.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 2 (d) 1
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 4 (b) 15 (c) 16 (d) 14
  23. 23.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 226 (c) 232 (d) 231
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 5 (b) 15 (c) 17 (d) 16
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 73? (a) 7 (b) 18 (c) 16 (d) 17
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 61? (a) 4 (b) 6 (c) 5 (d) 7
  27. 27.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 421 (b) 411 (c) 352 (d) 420
  28. 28.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 130 (c) 129 (d) 138
  29. 29.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  30. 30.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 564 (b) 565 (c) 448 (d) 555
  31. 31.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 369 (c) 379 (d) 378
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 94? (a) 18 (b) 19 (c) 9 (d) 20
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 18 (b) 19 (c) 7 (d) 17
  34. 34.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) 60 (b) 63 (c) 20 (d) 180
  35. 35.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 167 (c) 158 (d) 168
  36. 36.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  37. 37.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 303 (c) 294 (d) 274
  38. 38.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 86 (c) 96 (d) 95
  39. 39.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  40. 40.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4

Answer key

  1. 15
  2. 6
  3. 24
  4. 8
  5. 360
  6. 18
  7. 45
  8. 18
  9. 111
  10. 20
  11. 39
  12. 7
  13. 66
  14. 183
  15. 9
  16. 19
  17. 282
  18. 7
  19. 69
  20. 3
  21. 2
  22. 15
  23. 231
  24. 16
  25. 17
  26. 6
  27. 420
  28. 129
  29. 3
  30. 564
  31. 378
  32. 19
  33. 18
  34. 60
  35. 167
  36. 4
  37. 303
  38. 95
  39. 4
  40. 3

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