math puzzle

[milagros317]

It's been a long time since I posted a math puzzle here, so here is a new one with four parts.

1) Find five consecutive positive integers whose product is equal to the product of three consecutive integers.

2) Find six consecutive positive integers whose product is equal to the product of three consecutive integers.

3) Find seven consecutive positive integers whose product is equal to the product of four consecutive integers.

4) Find a different sequence of seven consecutive positive integers whose product is equal to the product of four consecutive integers.

Answers will be posted tomorrow evening.

Hint: If you solve 1), then 2) and 3) are easy.
Warning: 4) is difficult.

 

[FrenzyTickles]

I'm afraid my head just exploded, but thank you for sharing the brain fodder,
it would be worth learning this just to stave off dementia!!! 😀

 

[milagros317]

Solutions:

1)
a) Lowest solution: 1x2x3x4x5 = 120 = 4x5x6
b) Next solution: 2x3x4x5x6 = 720 = 8x9x10

2) Building on 1)b): 1x2x3x4x5x6 = 720 = 8x9x10

3) Building on 2): 1x2x3x4x5x6x7 = 5,040 = 7x8x9x10

4) 8x9x10x11x12x13x14 = 17,297,280 = 63x64x65x66