Which four consecutive odds, when multiplied together, give the product 6xxxxxx9?
Each x represents a digit, not necessarily the same.
the numbers cannot contain so they must end in 7,9,1,3 (note the product of these ends in 9). The mean of the numbers ends in 0, so call the product of the numbers (10x-3)(10x-1)(10x+1)(10x+3) which I don't feel like expanding, but its not much smaller than (10x)^4.
If x=10 the number will be just little bit under 100000000 and won't begin with a 6.
9^4=6561 so that will almost certainly do it
8^4=4096 which is too small
double-check with a calculator: 93*91*89*87=65529009
Extra work: Expanding the product shows why the product is so close to (10x)^4:
(100x^2-1)(100x^2-9)=10000x^4-100x^2+9
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Posted by Jer
on 2024-06-22 14:54:13 |
mostly mental reasoning
