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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 25 · 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 12? (a) 13 (b) 8 (c) 6 (d) 7
  2. 2.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) 48 (c) 45 (d) 135
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 5 (b) 15 (c) 17 (d) 16
  4. 4.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) 180 (b) 60 (c) 20 (d) 63
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 3 (b) 2 (c) 1 (d) 4
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 30? (a) 3 (b) 2 (c) 1 (d) 4
  7. 7.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
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 4 (b) 3 (c) 2 (d) 1
  9. 9.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 272 (b) 291 (c) 300 (d) 301
  10. 10.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 16 (b) 15 (c) 4 (d) 14
  12. 12.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) 6 (b) 21 (c) 54 (d) 18
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 5 (b) 16 (c) 17 (d) 15
  14. 14.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 388 (c) 378 (d) 330
  15. 15.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 95 (c) 96 (d) 104
  16. 16.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) 30 (c) 33 (d) 10
  17. 17.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 38 (c) 47 (d) 48
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 14 (b) 15 (c) 16 (d) 5
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 14 (d) 15
  20. 20.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) 189 (c) 21 (d) 66
  21. 21.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 496 (c) 402 (d) 495
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 7 (b) 8 (c) 6 (d) 5
  23. 23.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) 57 (d) 162
  24. 24.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) 27 (c) 24 (d) 72
  25. 25.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 3 (b) 5 (c) 4 (d) 2
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  28. 28.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 102 (c) 111 (d) 112
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 8 (b) 9 (c) 11 (d) 10
  30. 30.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 134 (c) 143 (d) 152
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 43? (a) 4 (b) 2 (c) 3 (d) 5
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 19 (b) 17 (c) 18 (d) 7
  33. 33.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 10 (d) 6
  34. 34.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 364 (c) 439 (d) 429
  35. 35.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 337 (b) 296 (c) 336 (d) 327
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 13 (b) 14 (c) 3 (d) 15
  37. 37.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 5 (d) 10
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 6 (b) 16 (c) 18 (d) 17
  39. 39.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 134 (c) 125 (d) 116
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 14 (b) 4 (c) 15 (d) 16

Answer key

  1. 7
  2. 45
  3. 16
  4. 60
  5. 3
  6. 3
  7. 36
  8. 3
  9. 300
  10. 5
  11. 15
  12. 18
  13. 16
  14. 387
  15. 95
  16. 30
  17. 47
  18. 15
  19. 15
  20. 63
  21. 495
  22. 7
  23. 54
  24. 24
  25. 3
  26. 4
  27. 2
  28. 111
  29. 10
  30. 143
  31. 4
  32. 18
  33. 7
  34. 438
  35. 336
  36. 14
  37. 4
  38. 17
  39. 125
  40. 15

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