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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 130 · 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 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) 171 (b) 57 (c) 19 (d) 60
  2. 2.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  3. 3.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 1 (d) 3
  4. 4.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 3 (d) 1
  5. 5.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 7 (d) 9
  6. 6.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 22 (c) 31 (d) 40
  7. 7.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) 16 (b) 144 (c) 51 (d) 48
  8. 8.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) 24 (b) 75 (c) 72 (d) 216
  9. 9.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 294 (c) 334 (d) 324
  10. 10.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) 11 (b) 33 (c) 36 (d) 99
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 2 (b) 3 (c) 4 (d) 5
  12. 12.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 351 (c) 352 (d) 342
  13. 13.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 202 (c) 186 (d) 195
  14. 14.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 310 (c) 348 (d) 358
  15. 15.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 79 (c) 70 (d) 80
  16. 16.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  17. 17.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) 624 (c) 625 (d) 615
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 8 (b) 20 (c) 19 (d) 18
  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) 13 (b) 42 (c) 117 (d) 39
  20. 20.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 411 (c) 346 (d) 412
  21. 21.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 4 (d) 6
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 1 (b) 4 (c) 3 (d) 2
  23. 23.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
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 60? (a) 15 (b) 6 (c) 16 (d) 17
  25. 25.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 415 (c) 414 (d) 348
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 5 (b) 3 (c) 6 (d) 4
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 19 (b) 18 (c) 8 (d) 20
  28. 28.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 277 (c) 267 (d) 256
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 2 (b) 4 (c) 3 (d) 5
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 18 (b) 8 (c) 19 (d) 20
  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) 320 (d) 363
  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) 10 (b) 30 (c) 33 (d) 90
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 15 (b) 5 (c) 16 (d) 17
  34. 34.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 556 (b) 442 (c) 555 (d) 546
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 94? (a) 20 (b) 18 (c) 19 (d) 9
  36. 36.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  37. 37.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 574 (b) 454 (c) 564 (d) 573
  38. 38.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 5 (b) 3 (c) 6 (d) 4
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 18 (b) 19 (c) 17 (d) 7

Answer key

  1. 57
  2. 3
  3. 2
  4. 2
  5. 8
  6. 31
  7. 48
  8. 72
  9. 333
  10. 33
  11. 4
  12. 351
  13. 195
  14. 357
  15. 79
  16. 5
  17. 624
  18. 19
  19. 39
  20. 411
  21. 5
  22. 3
  23. 45
  24. 16
  25. 414
  26. 5
  27. 19
  28. 276
  29. 4
  30. 19
  31. 372
  32. 30
  33. 16
  34. 555
  35. 19
  36. 4
  37. 573
  38. 3
  39. 5
  40. 18

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