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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 896 · 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 1 written when you write all the numbers from 1 to 59? (a) 17 (b) 15 (c) 5 (d) 16
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 17 (b) 6 (c) 16 (d) 18
  3. 3.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) 207 (d) 23
  4. 4.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) 21 (b) 54 (c) 18 (d) 6
  5. 5.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 250 (c) 238 (d) 240
  6. 6.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 26 (c) 36 (d) 35
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 3 (b) 6 (c) 4 (d) 5
  8. 8.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 261 (c) 252 (d) 246
  9. 9.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 62 (c) 53 (d) 54
  10. 10.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 349 (c) 339 (d) 304
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 9 (b) 20 (c) 18 (d) 19
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 16 (b) 17 (c) 6 (d) 18
  13. 13.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  14. 14.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 332 (c) 391 (d) 381
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 7 (b) 19 (c) 18 (d) 17
  16. 16.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 8 (d) 7
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 15 (b) 16 (c) 17 (d) 5
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 65? (a) 4 (b) 6 (c) 5 (d) 7
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 52? (a) 3 (b) 4 (c) 5 (d) 6
  20. 20.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 162 (c) 171 (d) 172
  21. 21.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  22. 22.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  23. 23.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 4 (d) 2
  24. 24.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 523 (c) 513 (d) 420
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 93? (a) 18 (b) 20 (c) 19 (d) 9
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 7 (b) 4 (c) 6 (d) 5
  27. 27.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 114 (c) 132 (d) 123
  28. 28.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 501 (c) 412 (d) 511
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 19 (b) 7 (c) 17 (d) 18
  30. 30.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) 189 (b) 63 (c) 66 (d) 21
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 8 (b) 7 (c) 9 (d) 6
  32. 32.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 428 (c) 525 (d) 535
  33. 33.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 61 (c) 52 (d) 70
  34. 34.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 17 (b) 18 (c) 7 (d) 19
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 21 (b) 19 (c) 9 (d) 20
  37. 37.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 303 (c) 294 (d) 274
  38. 38.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 402 (c) 346 (d) 411
  39. 39.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 58? (a) 4 (b) 6 (c) 5 (d) 3

Answer key

  1. 16
  2. 17
  3. 69
  4. 18
  5. 249
  6. 35
  7. 5
  8. 261
  9. 53
  10. 348
  11. 19
  12. 17
  13. 6
  14. 390
  15. 18
  16. 7
  17. 16
  18. 6
  19. 5
  20. 171
  21. 9
  22. 8
  23. 3
  24. 522
  25. 19
  26. 6
  27. 123
  28. 510
  29. 18
  30. 63
  31. 8
  32. 534
  33. 61
  34. 9
  35. 18
  36. 20
  37. 303
  38. 411
  39. 2
  40. 5

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