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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 151 · 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.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) 66 (c) 22 (d) 198
  2. 2.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  3. 3.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 531 (c) 540 (d) 541
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 5 (b) 4 (c) 6 (d) 7
  5. 5.The numbers 3 to 11 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) 24 (c) 63 (d) 7
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 70? (a) 6 (b) 8 (c) 9 (d) 7
  7. 7.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) 33 (c) 30 (d) 90
  8. 8.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) 24 (d) 27
  9. 9.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 73 (b) 74 (c) 64 (d) 82
  10. 10.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 435 (c) 436 (d) 362
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 86? (a) 8 (b) 20 (c) 18 (d) 19
  12. 12.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 285 (c) 286 (d) 276
  13. 13.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) 162 (b) 18 (c) 54 (d) 57
  14. 14.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 600 (c) 609 (d) 478
  15. 15.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) 15 (b) 5 (c) 18 (d) 45
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 18 (d) 7
  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) 38 (b) 56 (c) 48 (d) 47
  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) 240 (b) 252 (c) 243 (d) 253
  19. 19.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 80 (c) 79 (d) 88
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 73? (a) 17 (b) 16 (c) 18 (d) 7
  21. 21.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 265 (c) 255 (d) 248
  22. 22.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 42 (c) 41 (d) 32
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 5 (b) 6 (c) 3 (d) 4
  24. 24.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
  25. 25.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 428 (b) 534 (c) 525 (d) 535
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 6 (b) 15 (c) 16 (d) 17
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 17 (b) 18 (c) 19 (d) 8
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 4 (d) 1
  29. 29.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) 16 (b) 51 (c) 144 (d) 48
  30. 30.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 162 (c) 161 (d) 152
  31. 31.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) 189 (c) 66 (d) 63
  32. 32.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  33. 33.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 108 (c) 117 (d) 118
  34. 34.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  35. 35.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 411 (c) 420 (d) 421
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 18 (b) 19 (c) 8 (d) 20
  37. 37.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
  38. 38.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 220 (c) 213 (d) 223
  39. 39.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 72? (a) 8 (b) 7 (c) 10 (d) 11

Answer key

  1. 66
  2. 7
  3. 540
  4. 6
  5. 21
  6. 8
  7. 30
  8. 24
  9. 73
  10. 435
  11. 19
  12. 285
  13. 54
  14. 609
  15. 15
  16. 18
  17. 47
  18. 252
  19. 79
  20. 17
  21. 264
  22. 41
  23. 5
  24. 8
  25. 534
  26. 16
  27. 18
  28. 3
  29. 48
  30. 161
  31. 63
  32. 6
  33. 117
  34. 5
  35. 420
  36. 19
  37. 7
  38. 222
  39. 9
  40. 10

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