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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 217 · 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 71? (a) 7 (b) 18 (c) 16 (d) 17
  2. 2.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 104 (c) 103 (d) 112
  3. 3.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) 36 (d) 99
  4. 4.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) 15 (d) 5
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 5 (b) 3 (c) 4 (d) 2
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 3 (b) 2 (c) 4 (d) 5
  7. 7.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 475 (b) 388 (c) 465 (d) 474
  8. 8.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) 60 (b) 19 (c) 171 (d) 57
  9. 9.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  10. 10.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  11. 11.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 131 (c) 132 (d) 122
  12. 12.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
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 19 (b) 17 (c) 18 (d) 7
  14. 14.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 17 (b) 7 (c) 18 (d) 19
  16. 16.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 6 (d) 13
  17. 17.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 375 (b) 385 (c) 328 (d) 384
  18. 18.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) 176 (c) 185 (d) 186
  19. 19.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) 63 (d) 20
  20. 20.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 390 (c) 478 (d) 477
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 4 (b) 3 (c) 6 (d) 5
  22. 22.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 349 (c) 304 (d) 348
  23. 23.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) 66 (b) 21 (c) 63 (d) 189
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 61? (a) 5 (b) 7 (c) 6 (d) 4
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 2 (b) 4 (c) 3 (d) 1
  26. 26.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  27. 27.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 291 (c) 300 (d) 272
  28. 28.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 102 (c) 110 (d) 101
  29. 29.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 415 (c) 405 (d) 414
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 80? (a) 8 (b) 18 (c) 17 (d) 19
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 99? (a) 9 (b) 19 (c) 20 (d) 21
  32. 32.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 452 (b) 570 (c) 571 (d) 561
  33. 33.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 12 (d) 7
  34. 34.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
  35. 35.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 152 (c) 160 (d) 151
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 6 (b) 5 (c) 8 (d) 7
  37. 37.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 319 (b) 318 (c) 309 (d) 284
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 16 (b) 17 (c) 18 (d) 7
  39. 39.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 573 (c) 583 (d) 460
  40. 40.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

Answer key

  1. 17
  2. 103
  3. 33
  4. 15
  5. 4
  6. 4
  7. 474
  8. 57
  9. 6
  10. 9
  11. 131
  12. 45
  13. 18
  14. 6
  15. 18
  16. 7
  17. 384
  18. 185
  19. 60
  20. 477
  21. 5
  22. 348
  23. 63
  24. 6
  25. 3
  26. 3
  27. 300
  28. 101
  29. 414
  30. 18
  31. 20
  32. 570
  33. 8
  34. 48
  35. 151
  36. 7
  37. 318
  38. 17
  39. 582
  40. 161

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