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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 942 · 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.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 170 (c) 169 (d) 160
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 5 (b) 8 (c) 10 (d) 11
  3. 3.The numbers 10 to 18 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) 14 (c) 126 (d) 42
  4. 4.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 391 (b) 381 (c) 390 (d) 332
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 20 (b) 19 (c) 9 (d) 21
  6. 6.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) 8 (b) 72 (c) 24 (d) 27
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 4 (b) 3 (c) 2 (d) 5
  8. 8.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) 21 (b) 66 (c) 189 (d) 63
  9. 9.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) 18 (c) 5 (d) 15
  10. 10.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 580 (c) 570 (d) 579
  11. 11.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 1 (d) 18
  12. 12.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 75? (a) 17 (b) 19 (c) 7 (d) 18
  14. 14.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 264 (c) 265 (d) 248
  15. 15.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 540 (c) 541 (d) 432
  16. 16.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 2 (d) 4
  17. 17.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 622 (c) 612 (d) 621
  18. 18.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) 117 (d) 42
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 6 (b) 4 (c) 3 (d) 5
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 14 (b) 4 (c) 15 (d) 13
  21. 21.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) 24 (b) 75 (c) 72 (d) 216
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 9 (b) 21 (c) 20 (d) 19
  23. 23.The numbers 16 to 24 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) 180 (c) 60 (d) 20
  24. 24.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
  25. 25.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) 72 (b) 69 (c) 23 (d) 207
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 4 (b) 1 (c) 3 (d) 2
  27. 27.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) 19 (c) 171 (d) 60
  28. 28.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) 393 (d) 394
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 21 (b) 19 (c) 20 (d) 9
  30. 30.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 5 (d) 3
  31. 31.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 550 (c) 540 (d) 549
  32. 32.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 637 (b) 627 (c) 496 (d) 636
  33. 33.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
  34. 34.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) 15 (b) 45 (c) 135 (d) 48
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 2 (b) 1 (c) 4 (d) 3
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 89? (a) 19 (b) 20 (c) 8 (d) 18
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 3 (d) 2
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 4 (b) 6 (c) 3 (d) 5
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 18 (b) 16 (c) 7 (d) 17
  40. 40.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9

Answer key

  1. 169
  2. 10
  3. 42
  4. 390
  5. 20
  6. 24
  7. 4
  8. 63
  9. 15
  10. 579
  11. 2
  12. 2
  13. 18
  14. 264
  15. 540
  16. 3
  17. 621
  18. 39
  19. 5
  20. 14
  21. 72
  22. 20
  23. 60
  24. 3
  25. 69
  26. 3
  27. 57
  28. 393
  29. 20
  30. 4
  31. 549
  32. 636
  33. 7
  34. 45
  35. 3
  36. 19
  37. 3
  38. 5
  39. 17
  40. 9

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