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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 184 · 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 3? (a) 2 (b) 10 (c) 3 (d) 4
  2. 2.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  4. 4.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 81 (c) 27 (d) 9
  5. 5.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 13 (b) 15 (c) 4 (d) 14
  7. 7.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 11 (d) 8
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 13 (b) 15 (c) 14 (d) 3
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 16 (b) 14 (c) 5 (d) 15
  10. 10.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 426 (c) 532 (d) 531
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 17 (b) 18 (c) 7 (d) 16
  12. 12.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 63 (b) 72 (c) 64 (d) 54
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 19 (b) 7 (c) 18 (d) 17
  14. 14.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  15. 15.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 270 (c) 297 (d) 288
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 9 (b) 19 (c) 20 (d) 21
  17. 17.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 486 (c) 496 (d) 495
  18. 18.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 14 (d) 7
  19. 19.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) 8 (c) 72 (d) 24
  20. 20.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) 36 (b) 99 (c) 33 (d) 11
  21. 21.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) 144 (b) 16 (c) 51 (d) 48
  22. 22.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 68 (c) 67 (d) 76
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 14 (b) 4 (c) 15 (d) 16
  24. 24.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 5 (b) 4 (c) 2 (d) 3
  26. 26.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) 69 (b) 198 (c) 22 (d) 66
  27. 27.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) 18 (c) 54 (d) 162
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 15 (b) 12 (c) 7 (d) 14
  29. 29.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 459 (b) 450 (c) 460 (d) 378
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 31? (a) 3 (b) 4 (c) 1 (d) 2
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 93? (a) 9 (b) 18 (c) 20 (d) 19
  32. 32.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 469 (b) 384 (c) 459 (d) 468
  33. 33.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 501 (c) 510 (d) 511
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 6 (b) 4 (c) 7 (d) 5
  35. 35.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 369 (c) 360 (d) 370
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 1 (b) 3 (c) 2 (d) 4
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 19 (b) 17 (c) 7 (d) 18
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 19 (b) 9 (c) 20 (d) 21
  39. 39.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) 126 (b) 42 (c) 45 (d) 14
  40. 40.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10

Answer key

  1. 3
  2. 7
  3. 5
  4. 27
  5. 9
  6. 14
  7. 9
  8. 14
  9. 15
  10. 531
  11. 17
  12. 63
  13. 18
  14. 2
  15. 297
  16. 20
  17. 495
  18. 6
  19. 24
  20. 33
  21. 48
  22. 67
  23. 15
  24. 4
  25. 4
  26. 66
  27. 54
  28. 14
  29. 459
  30. 3
  31. 19
  32. 468
  33. 510
  34. 6
  35. 369
  36. 3
  37. 18
  38. 20
  39. 42
  40. 6

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