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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 843 · 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 times is the digit 2 written when you write all the numbers from 1 to 71? (a) 7 (b) 18 (c) 16 (d) 17
  2. 2.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 8 (d) 10
  3. 3.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 3 (b) 6 (c) 5 (d) 4
  5. 5.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 320 (b) 373 (c) 363 (d) 372
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 38? (a) 5 (b) 4 (c) 2 (d) 3
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 17 (b) 19 (c) 8 (d) 18
  8. 8.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) 198 (b) 22 (c) 69 (d) 66
  9. 9.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 181 (c) 182 (d) 172
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 90? (a) 20 (b) 19 (c) 9 (d) 18
  11. 11.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) 63 (b) 21 (c) 189 (d) 66
  12. 12.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 392 (b) 481 (c) 471 (d) 480
  13. 13.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 289 (c) 288 (d) 279
  14. 14.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 334 (c) 384 (d) 394
  15. 15.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) 48 (b) 15 (c) 45 (d) 135
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 16 (b) 14 (c) 5 (d) 15
  17. 17.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 232 (c) 241 (d) 240
  18. 18.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) 30 (c) 33 (d) 90
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 2 (b) 1 (c) 4 (d) 3
  20. 20.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) 24 (c) 8 (d) 72
  21. 21.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 4 (b) 1 (c) 2 (d) 3
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 52? (a) 3 (b) 5 (c) 6 (d) 4
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 16 (b) 17 (c) 18 (d) 7
  25. 25.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 19 (b) 8 (c) 17 (d) 18
  27. 27.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) 45 (b) 5 (c) 18 (d) 15
  28. 28.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) 54 (c) 162 (d) 57
  29. 29.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) 57 (b) 171 (c) 60 (d) 19
  30. 30.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 586 (c) 585 (d) 462
  31. 31.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 128 (c) 120 (d) 119
  32. 32.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 169 (c) 178 (d) 160
  33. 33.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 358 (c) 420 (d) 430
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 17 (b) 18 (c) 8 (d) 19
  35. 35.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 423 (c) 432 (d) 433
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 1 (b) 4 (c) 2 (d) 3
  37. 37.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  38. 38.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 9 (d) 12
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 6 (b) 17 (c) 18 (d) 16
  40. 40.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2

Answer key

  1. 17
  2. 7
  3. 8
  4. 5
  5. 372
  6. 4
  7. 18
  8. 66
  9. 181
  10. 19
  11. 63
  12. 480
  13. 288
  14. 393
  15. 45
  16. 15
  17. 240
  18. 30
  19. 3
  20. 24
  21. 3
  22. 3
  23. 5
  24. 17
  25. 5
  26. 18
  27. 15
  28. 54
  29. 57
  30. 585
  31. 119
  32. 169
  33. 429
  34. 18
  35. 432
  36. 3
  37. 9
  38. 8
  39. 17
  40. 3

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