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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 686 · 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 2? (a) 10 (b) 2 (c) 3 (d) 1
  2. 2.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) 198 (c) 22 (d) 69
  3. 3.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 236 (b) 237 (c) 247 (d) 246
  4. 4.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) 57 (b) 54 (c) 18 (d) 162
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 21 (b) 19 (c) 9 (d) 20
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 88? (a) 19 (b) 20 (c) 18 (d) 8
  7. 7.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  8. 8.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 13 (b) 14 (c) 15 (d) 3
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 65? (a) 18 (b) 6 (c) 16 (d) 17
  11. 11.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 2 (b) 3 (c) 5 (d) 4
  13. 13.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 9 (d) 11
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 19 (d) 18
  15. 15.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 334 (c) 394 (d) 393
  16. 16.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) 18 (c) 6 (d) 21
  17. 17.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 80 (c) 71 (d) 72
  18. 18.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) 11 (b) 99 (c) 36 (d) 33
  19. 19.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 181 (b) 190 (c) 172 (d) 182
  20. 20.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) 7 (c) 21 (d) 63
  21. 21.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  22. 22.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 388 (c) 387 (d) 378
  23. 23.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) 10 (b) 33 (c) 90 (d) 30
  24. 24.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 472 (c) 386 (d) 471
  25. 25.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 175 (b) 184 (c) 166 (d) 176
  26. 26.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) 39 (b) 13 (c) 42 (d) 117
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 19 (b) 9 (c) 20 (d) 18
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 86? (a) 20 (b) 8 (c) 18 (d) 19
  29. 29.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) 144 (c) 48 (d) 51
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 74? (a) 16 (b) 17 (c) 7 (d) 18
  31. 31.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 4 (d) 6
  32. 32.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 580 (b) 579 (c) 570 (d) 458
  33. 33.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 570 (c) 571 (d) 452
  34. 34.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 271 (b) 252 (c) 261 (d) 270
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 3 (b) 11 (c) 12 (d) 10
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 17 (b) 15 (c) 5 (d) 16
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 21 (b) 19 (c) 9 (d) 20
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 18 (b) 19 (c) 7 (d) 17
  39. 39.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  40. 40.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) 72 (b) 8 (c) 24 (d) 27

Answer key

  1. 2
  2. 66
  3. 246
  4. 54
  5. 20
  6. 19
  7. 8
  8. 8
  9. 14
  10. 17
  11. 4
  12. 4
  13. 9
  14. 19
  15. 393
  16. 18
  17. 71
  18. 33
  19. 181
  20. 21
  21. 3
  22. 387
  23. 30
  24. 471
  25. 175
  26. 39
  27. 19
  28. 19
  29. 48
  30. 17
  31. 5
  32. 579
  33. 570
  34. 270
  35. 11
  36. 16
  37. 20
  38. 18
  39. 7
  40. 24

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