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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 136 · 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 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) 7 (b) 24 (c) 21 (d) 63
  2. 2.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 2 (b) 4 (c) 1 (d) 3
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 69? (a) 18 (b) 17 (c) 6 (d) 16
  5. 5.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) 69 (c) 23 (d) 72
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 21 (b) 19 (c) 20 (d) 9
  7. 7.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
  8. 8.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 358 (c) 430 (d) 429
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 3 (b) 14 (c) 15 (d) 13
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  11. 11.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) 75 (b) 216 (c) 72 (d) 24
  12. 12.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  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) 69 (b) 22 (c) 198 (d) 66
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 15 (b) 17 (c) 5 (d) 16
  15. 15.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 49 (b) 58 (c) 40 (d) 50
  16. 16.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 177 (b) 178 (c) 168 (d) 186
  17. 17.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 6 (b) 5 (c) 4 (d) 3
  19. 19.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) 17 (b) 54 (c) 153 (d) 51
  20. 20.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 399 (c) 344 (d) 409
  21. 21.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
  22. 22.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  23. 23.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  24. 24.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 586 (b) 462 (c) 585 (d) 576
  25. 25.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
  26. 26.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 244 (c) 243 (d) 351
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 74? (a) 8 (b) 6 (c) 5 (d) 7
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 8 (b) 20 (c) 19 (d) 18
  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) 159 (b) 160 (c) 168 (d) 150
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 8 (b) 9 (c) 7 (d) 10
  31. 31.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 7 (b) 4 (c) 3 (d) 6
  33. 33.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 520 (c) 418 (d) 519
  34. 34.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 343 (c) 342 (d) 300
  35. 35.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) 36 (b) 11 (c) 99 (d) 33
  36. 36.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 494 (b) 624 (c) 634 (d) 633
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 4 (b) 1 (c) 2 (d) 3
  38. 38.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 4 (d) 15
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 8 (b) 20 (c) 18 (d) 19
  40. 40.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) 15 (c) 48 (d) 135

Answer key

  1. 21
  2. 8
  3. 3
  4. 17
  5. 69
  6. 20
  7. 9
  8. 429
  9. 14
  10. 3
  11. 72
  12. 2
  13. 66
  14. 16
  15. 49
  16. 177
  17. 6
  18. 5
  19. 51
  20. 408
  21. 9
  22. 5
  23. 2
  24. 585
  25. 39
  26. 243
  27. 7
  28. 19
  29. 159
  30. 9
  31. 6
  32. 6
  33. 519
  34. 342
  35. 33
  36. 633
  37. 3
  38. 5
  39. 19
  40. 45

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