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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 891 · 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 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) 42 (b) 39 (c) 13 (d) 117
  2. 2.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 483 (c) 493 (d) 492
  3. 3.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 185 (b) 186 (c) 176 (d) 194
  4. 4.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 175 (c) 166 (d) 176
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  6. 6.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 7 (d) 9
  7. 7.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 59 (c) 68 (d) 60
  8. 8.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
  9. 9.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
  10. 10.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 3 (d) 5
  11. 11.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 277 (b) 256 (c) 276 (d) 267
  12. 12.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) 63 (b) 24 (c) 21 (d) 7
  13. 13.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 50 (c) 58 (d) 49
  14. 14.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) 18 (b) 45 (c) 5 (d) 15
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 17 (b) 16 (c) 5 (d) 15
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 18 (b) 9 (c) 19 (d) 20
  17. 17.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) 525 (c) 535 (d) 534
  18. 18.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 19 (d) 20
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 77? (a) 7 (b) 17 (c) 18 (d) 19
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 4 (b) 2 (c) 3 (d) 1
  22. 22.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 9 (b) 27 (c) 30 (d) 81
  23. 23.The numbers 13 to 21 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) 153 (c) 51 (d) 17
  24. 24.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 459 (b) 468 (c) 469 (d) 384
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 5 (b) 6 (c) 4 (d) 7
  26. 26.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 75 (c) 24 (d) 72
  27. 27.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) 135 (d) 45
  28. 28.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 8 (d) 10
  29. 29.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) 24 (b) 72 (c) 8 (d) 27
  30. 30.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 426 (c) 435 (d) 362
  31. 31.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 373 (c) 363 (d) 320
  32. 32.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) 90 (c) 10 (d) 30
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 4 (b) 5 (c) 6 (d) 3
  34. 34.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 427 (b) 417 (c) 426 (d) 356
  35. 35.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  36. 36.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 6 (d) 7
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 38? (a) 2 (b) 3 (c) 4 (d) 5
  38. 38.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 4 (d) 6
  39. 39.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 357 (c) 367 (d) 316
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 16 (b) 17 (c) 18 (d) 7

Answer key

  1. 39
  2. 492
  3. 185
  4. 175
  5. 6
  6. 8
  7. 59
  8. 69
  9. 2
  10. 4
  11. 276
  12. 21
  13. 49
  14. 15
  15. 16
  16. 19
  17. 534
  18. 2
  19. 19
  20. 18
  21. 3
  22. 27
  23. 51
  24. 468
  25. 6
  26. 72
  27. 45
  28. 9
  29. 24
  30. 435
  31. 372
  32. 30
  33. 5
  34. 426
  35. 4
  36. 7
  37. 4
  38. 5
  39. 366
  40. 17

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