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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 837 · 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 17? (a) 1 (b) 18 (c) 2 (d) 3
  2. 2.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) 99 (b) 36 (c) 11 (d) 33
  3. 3.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 7 (d) 8
  4. 4.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 53? (a) 5 (b) 15 (c) 16 (d) 14
  6. 6.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 501 (b) 510 (c) 511 (d) 412
  7. 7.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 12 (c) 39 (d) 36
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 19 (b) 8 (c) 17 (d) 18
  9. 9.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 571 (b) 452 (c) 570 (d) 561
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 68? (a) 5 (b) 8 (c) 6 (d) 7
  11. 11.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 352 (c) 420 (d) 421
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 2 (b) 4 (c) 3 (d) 1
  13. 13.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) 13 (b) 117 (c) 39 (d) 42
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 3 (b) 4 (c) 2 (d) 5
  15. 15.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  16. 16.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 307 (b) 297 (c) 276 (d) 306
  17. 17.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 54 (c) 18 (d) 162
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 72? (a) 10 (b) 7 (c) 8 (d) 11
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 7 (b) 5 (c) 6 (d) 4
  20. 20.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) 90 (b) 30 (c) 33 (d) 10
  21. 21.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 99 (c) 90 (d) 108
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 14 (b) 15 (c) 4 (d) 16
  23. 23.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 459 (c) 469 (d) 384
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 7 (b) 5 (c) 6 (d) 4
  25. 25.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 272 (c) 301 (d) 300
  26. 26.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 379 (b) 369 (c) 378 (d) 324
  27. 27.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 488 (b) 615 (c) 625 (d) 624
  28. 28.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
  29. 29.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 601 (b) 472 (c) 591 (d) 600
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 16 (b) 17 (c) 7 (d) 18
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 17 (b) 18 (c) 16 (d) 6
  32. 32.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
  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.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) 21 (b) 63 (c) 7 (d) 24
  35. 35.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
  36. 36.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) 30 (b) 81 (c) 9 (d) 27
  37. 37.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) 21 (b) 66 (c) 63 (d) 189
  38. 38.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 5 (b) 2 (c) 3 (d) 4
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 65? (a) 5 (b) 4 (c) 7 (d) 6

Answer key

  1. 2
  2. 33
  3. 7
  4. 7
  5. 15
  6. 510
  7. 36
  8. 18
  9. 570
  10. 7
  11. 420
  12. 3
  13. 39
  14. 4
  15. 6
  16. 306
  17. 54
  18. 10
  19. 6
  20. 30
  21. 99
  22. 15
  23. 468
  24. 6
  25. 300
  26. 378
  27. 624
  28. 3
  29. 600
  30. 17
  31. 17
  32. 4
  33. 5
  34. 21
  35. 5
  36. 27
  37. 63
  38. 4
  39. 4
  40. 6

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