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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 402 · 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 2? (a) 10 (b) 1 (c) 3 (d) 2
  2. 2.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) 54 (b) 21 (c) 6 (d) 18
  3. 3.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) 5 (c) 15 (d) 18
  4. 4.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 314 (c) 363 (d) 354
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 17 (b) 18 (c) 6 (d) 16
  6. 6.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 9 (d) 10
  7. 7.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 529 (c) 519 (d) 528
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 13 (b) 11 (c) 8 (d) 14
  9. 9.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 3 (d) 17
  10. 10.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  11. 11.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 195 (c) 204 (d) 205
  12. 12.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 381 (c) 372 (d) 326
  13. 13.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) 207 (c) 69 (d) 23
  14. 14.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 470 (b) 598 (c) 597 (d) 588
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 4 (b) 9 (c) 8 (d) 6
  16. 16.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) 24 (b) 63 (c) 7 (d) 21
  17. 17.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 265 (c) 248 (d) 264
  18. 18.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 330 (c) 331 (d) 321
  19. 19.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 522 (c) 523 (d) 513
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 66? (a) 5 (b) 4 (c) 7 (d) 6
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 17 (b) 18 (c) 19 (d) 8
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 10 (b) 7 (c) 8 (d) 9
  23. 23.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) 439 (c) 429 (d) 364
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 5 (b) 3 (c) 2 (d) 4
  25. 25.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 238 (b) 228 (c) 237 (d) 230
  26. 26.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  27. 27.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) 72 (d) 24
  28. 28.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  29. 29.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) 171 (b) 19 (c) 57 (d) 60
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 99? (a) 20 (b) 9 (c) 19 (d) 21
  31. 31.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 39 (c) 42 (d) 13
  32. 32.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 70 (c) 69 (d) 60
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 8 (b) 17 (c) 19 (d) 18
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 94? (a) 20 (b) 18 (c) 19 (d) 9
  35. 35.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) 33 (b) 30 (c) 90 (d) 10
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 5 (b) 2 (c) 4 (d) 3
  37. 37.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 328 (c) 385 (d) 375
  38. 38.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 100 (c) 108 (d) 99
  39. 39.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
  40. 40.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 5 (d) 3

Answer key

  1. 2
  2. 18
  3. 15
  4. 363
  5. 17
  6. 9
  7. 528
  8. 13
  9. 3
  10. 5
  11. 204
  12. 381
  13. 69
  14. 597
  15. 8
  16. 21
  17. 264
  18. 330
  19. 522
  20. 6
  21. 18
  22. 9
  23. 438
  24. 4
  25. 237
  26. 8
  27. 24
  28. 6
  29. 57
  30. 20
  31. 39
  32. 69
  33. 18
  34. 19
  35. 30
  36. 4
  37. 384
  38. 99
  39. 5
  40. 4

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