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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 117 · 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 4 written when you write all the numbers from 1 to 52? (a) 16 (b) 15 (c) 14 (d) 5
  2. 2.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
  3. 3.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) 66 (c) 69 (d) 22
  4. 4.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 194 (b) 186 (c) 185 (d) 176
  5. 5.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  6. 6.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 72 (c) 62 (d) 71
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5
  8. 8.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
  9. 9.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 618 (c) 628 (d) 627
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 21 (b) 20 (c) 9 (d) 19
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 63? (a) 8 (b) 11 (c) 10 (d) 6
  12. 12.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) 33 (c) 99 (d) 36
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 8 (b) 19 (c) 20 (d) 18
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 98? (a) 20 (b) 9 (c) 19 (d) 21
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 8 (b) 18 (c) 19 (d) 20
  16. 16.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 7 (d) 6
  17. 17.The numbers 8 to 16 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) 108 (c) 12 (d) 36
  18. 18.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 253 (c) 240 (d) 243
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 64? (a) 16 (b) 6 (c) 18 (d) 17
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 18 (b) 7 (c) 17 (d) 16
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 6 (b) 8 (c) 5 (d) 7
  22. 22.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 550 (b) 540 (c) 549 (d) 438
  23. 23.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 8 (d) 7
  24. 24.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 488 (b) 625 (c) 615 (d) 624
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 7 (b) 18 (c) 16 (d) 17
  26. 26.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) 69 (b) 72 (c) 23 (d) 207
  27. 27.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  28. 28.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) 18 (c) 54 (d) 6
  29. 29.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) 27 (d) 24
  30. 30.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 18 (b) 19 (c) 8 (d) 17
  32. 32.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 14 (b) 13 (c) 4 (d) 15
  34. 34.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 400 (c) 390 (d) 338
  35. 35.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  36. 36.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) 216 (b) 75 (c) 72 (d) 24
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 5 (b) 2 (c) 4 (d) 3
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 3 (b) 5 (c) 4 (d) 6
  39. 39.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 442 (c) 366 (d) 441
  40. 40.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 472 (c) 601 (d) 600

Answer key

  1. 15
  2. 2
  3. 66
  4. 185
  5. 5
  6. 71
  7. 4
  8. 8
  9. 627
  10. 20
  11. 10
  12. 33
  13. 19
  14. 20
  15. 19
  16. 6
  17. 36
  18. 252
  19. 17
  20. 17
  21. 7
  22. 549
  23. 7
  24. 624
  25. 17
  26. 69
  27. 9
  28. 18
  29. 24
  30. 2
  31. 18
  32. 5
  33. 14
  34. 399
  35. 7
  36. 72
  37. 4
  38. 5
  39. 441
  40. 600

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