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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 413 · 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 15? (a) 16 (b) 3 (c) 5 (d) 4
  2. 2.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) 5 (b) 15 (c) 18 (d) 45
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 7 (b) 8 (c) 6 (d) 5
  4. 4.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
  5. 5.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) 48 (b) 45 (c) 135 (d) 15
  6. 6.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 5 (d) 10
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 8 (b) 10 (c) 7 (d) 9
  8. 8.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) 51 (c) 17 (d) 153
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 5 (b) 7 (c) 6 (d) 8
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 18 (b) 17 (c) 6 (d) 16
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 17 (b) 5 (c) 16 (d) 15
  12. 12.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 441 (c) 451 (d) 450
  13. 13.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 225 (b) 235 (c) 228 (d) 234
  14. 14.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 283 (b) 282 (c) 260 (d) 273
  15. 15.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 267 (c) 258 (d) 268
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 5 (b) 6 (c) 7 (d) 4
  17. 17.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 10 (b) 12 (c) 7 (d) 13
  19. 19.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) 13 (c) 39 (d) 117
  20. 20.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  21. 21.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 390 (c) 332 (d) 391
  22. 22.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) 462 (c) 586 (d) 585
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 5 (b) 2 (c) 4 (d) 3
  24. 24.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) 6 (c) 18 (d) 21
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 52? (a) 14 (b) 5 (c) 15 (d) 16
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 16 (b) 7 (c) 17 (d) 18
  27. 27.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) 21 (c) 24 (d) 7
  28. 28.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 231 (c) 232 (d) 226
  29. 29.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) 51 (b) 16 (c) 48 (d) 144
  30. 30.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
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 77? (a) 5 (b) 8 (c) 6 (d) 7
  32. 32.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 154 (c) 136 (d) 145
  33. 33.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) 60 (b) 63 (c) 20 (d) 180
  34. 34.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 438 (c) 439 (d) 364
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 6 (b) 4 (c) 5 (d) 3
  36. 36.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
  37. 37.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 397 (b) 396 (c) 336 (d) 387
  38. 38.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  39. 39.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 380 (b) 453 (c) 462 (d) 463
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 21 (b) 9 (c) 20 (d) 19

Answer key

  1. 4
  2. 15
  3. 7
  4. 2
  5. 45
  6. 4
  7. 9
  8. 51
  9. 7
  10. 17
  11. 16
  12. 450
  13. 234
  14. 282
  15. 267
  16. 6
  17. 9
  18. 12
  19. 39
  20. 5
  21. 390
  22. 585
  23. 4
  24. 18
  25. 15
  26. 17
  27. 21
  28. 231
  29. 48
  30. 69
  31. 7
  32. 145
  33. 60
  34. 438
  35. 5
  36. 8
  37. 396
  38. 2
  39. 462
  40. 20

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