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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 954 · 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 5? (a) 6 (b) 4 (c) 5 (d) 10
  2. 2.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 4 (d) 6
  3. 3.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 5 (d) 4
  4. 4.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 476 (c) 597 (d) 607
  5. 5.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 354 (c) 314 (d) 364
  6. 6.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  7. 7.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 585 (c) 586 (d) 462
  8. 8.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 17 (b) 19 (c) 18 (d) 7
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 18 (b) 17 (c) 6 (d) 16
  11. 11.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) 48 (b) 144 (c) 16 (d) 51
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 8 (b) 18 (c) 19 (d) 20
  13. 13.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) 18 (d) 15
  14. 14.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  15. 15.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7
  16. 16.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 478 (c) 468 (d) 390
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 79? (a) 17 (b) 19 (c) 7 (d) 18
  18. 18.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) 20 (b) 63 (c) 60 (d) 180
  19. 19.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 22 (b) 31 (c) 40 (d) 32
  20. 20.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 483 (c) 394 (d) 474
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 16 (b) 17 (c) 6 (d) 18
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 7 (b) 8 (c) 6 (d) 9
  23. 23.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  24. 24.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 351 (c) 244 (d) 243
  25. 25.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 88 (c) 78 (d) 87
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 53? (a) 16 (b) 5 (c) 14 (d) 15
  27. 27.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 504 (b) 414 (c) 513 (d) 514
  28. 28.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 4 (b) 5 (c) 2 (d) 3
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 6 (b) 7 (c) 5 (d) 4
  31. 31.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 171 (b) 180 (c) 162 (d) 172
  32. 32.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 378 (c) 330 (d) 387
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 18 (b) 9 (c) 20 (d) 19
  34. 34.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 292 (c) 321 (d) 331
  35. 35.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) 19 (b) 171 (c) 60 (d) 57
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 16 (b) 13 (c) 8 (d) 15
  37. 37.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 135 (b) 126 (c) 136 (d) 144
  38. 38.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) 30 (b) 10 (c) 33 (d) 90
  39. 39.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) 153 (b) 54 (c) 17 (d) 51
  40. 40.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1

Answer key

  1. 5
  2. 5
  3. 4
  4. 606
  5. 363
  6. 4
  7. 585
  8. 3
  9. 18
  10. 17
  11. 48
  12. 19
  13. 15
  14. 6
  15. 6
  16. 477
  17. 18
  18. 60
  19. 31
  20. 483
  21. 17
  22. 8
  23. 8
  24. 243
  25. 87
  26. 15
  27. 513
  28. 9
  29. 4
  30. 6
  31. 171
  32. 387
  33. 19
  34. 330
  35. 57
  36. 15
  37. 135
  38. 30
  39. 51
  40. 2

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