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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 106 · 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 7? (a) 6 (b) 8 (c) 10 (d) 7
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 18 (b) 17 (c) 7 (d) 19
  3. 3.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  4. 4.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 178 (c) 188 (d) 187
  5. 5.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 153 (c) 144 (d) 162
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 5 (b) 4 (c) 2 (d) 3
  7. 7.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 296 (c) 337 (d) 327
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 5 (b) 16 (c) 17 (d) 15
  9. 9.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  10. 10.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) 69 (d) 22
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 13 (b) 15 (c) 14 (d) 4
  12. 12.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 553 (c) 552 (d) 440
  13. 13.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) 27 (b) 72 (c) 8 (d) 24
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 15 (b) 16 (c) 4 (d) 14
  15. 15.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
  16. 16.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
  17. 17.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 179 (c) 188 (d) 180
  18. 18.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) 144 (d) 51
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 86? (a) 20 (b) 18 (c) 8 (d) 19
  20. 20.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
  21. 21.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3
  22. 22.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 8 (d) 13
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 5 (b) 4 (c) 6 (d) 3
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 93? (a) 18 (b) 20 (c) 19 (d) 9
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 6 (b) 17 (c) 18 (d) 16
  26. 26.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  27. 27.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) 117 (b) 42 (c) 13 (d) 39
  28. 28.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  29. 29.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 10 (d) 7
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 3 (b) 2 (c) 1 (d) 4
  31. 31.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 328 (c) 290 (d) 327
  32. 32.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  33. 33.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 120 (c) 130 (d) 129
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 3 (b) 5 (c) 6 (d) 4
  35. 35.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 362 (c) 435 (d) 426
  36. 36.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 270 (c) 279 (d) 280
  37. 37.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 240 (c) 238 (d) 249
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 7 (b) 17 (c) 19 (d) 18
  39. 39.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 360 (c) 433 (d) 423
  40. 40.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) 21 (b) 54 (c) 18 (d) 6

Answer key

  1. 7
  2. 18
  3. 9
  4. 187
  5. 153
  6. 4
  7. 336
  8. 16
  9. 5
  10. 66
  11. 14
  12. 552
  13. 24
  14. 15
  15. 30
  16. 3
  17. 179
  18. 48
  19. 19
  20. 9
  21. 2
  22. 7
  23. 5
  24. 19
  25. 17
  26. 2
  27. 39
  28. 8
  29. 6
  30. 3
  31. 327
  32. 8
  33. 129
  34. 5
  35. 435
  36. 279
  37. 249
  38. 18
  39. 432
  40. 18

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