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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 900 · 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) 5 (b) 16 (c) 3 (d) 4
  2. 2.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) 45 (b) 48 (c) 135 (d) 15
  3. 3.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) 81 (b) 9 (c) 27 (d) 30
  4. 4.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 223 (b) 220 (c) 222 (d) 213
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 16 (b) 6 (c) 17 (d) 18
  6. 6.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  7. 7.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  8. 8.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 312 (c) 280 (d) 313
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 17 (b) 15 (c) 5 (d) 16
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 18 (b) 19 (c) 17 (d) 7
  11. 11.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) 561 (d) 570
  12. 12.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 332 (c) 391 (d) 381
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 5 (b) 2 (c) 4 (d) 3
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 33? (a) 8 (b) 9 (c) 3 (d) 7
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 17 (b) 7 (c) 19 (d) 18
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 16 (b) 6 (c) 18 (d) 17
  17. 17.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 9 (b) 20 (c) 19 (d) 21
  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) 180 (d) 60
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 13 (b) 11 (c) 3 (d) 12
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 74? (a) 19 (b) 7 (c) 17 (d) 18
  21. 21.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
  22. 22.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 588 (b) 470 (c) 597 (d) 598
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 3 (b) 4 (c) 2 (d) 1
  24. 24.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 9 (b) 19 (c) 21 (d) 20
  26. 26.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
  27. 27.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 64? (a) 16 (b) 15 (c) 17 (d) 6
  29. 29.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 357 (c) 310 (d) 358
  30. 30.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 102 (c) 110 (d) 101
  31. 31.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 336 (c) 397 (d) 387
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 5 (b) 10 (c) 7 (d) 9
  33. 33.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 261 (c) 271 (d) 252
  34. 34.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 187 (b) 188 (c) 178 (d) 196
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 5 (b) 3 (c) 4 (d) 2
  36. 36.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 324 (c) 379 (d) 369
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 18 (b) 7 (c) 19 (d) 17
  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) 90 (b) 10 (c) 30 (d) 33
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 15 (b) 16 (c) 14 (d) 4
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 5 (b) 17 (c) 16 (d) 15

Answer key

  1. 4
  2. 45
  3. 27
  4. 222
  5. 17
  6. 9
  7. 8
  8. 312
  9. 16
  10. 18
  11. 570
  12. 390
  13. 4
  14. 8
  15. 18
  16. 17
  17. 20
  18. 60
  19. 12
  20. 18
  21. 3
  22. 597
  23. 3
  24. 3
  25. 20
  26. 48
  27. 9
  28. 16
  29. 357
  30. 101
  31. 396
  32. 9
  33. 270
  34. 187
  35. 4
  36. 378
  37. 18
  38. 30
  39. 15
  40. 16

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