The math riddle:
For those sick of these math posts, I apologize. This is for anyone still interested..
The question I can't seem to answer is why in the world does the $21m figure divide by both 1170 and 560? Neither of those numbers are random as they both relate to the expected TSA order. And, they don't appear to be mathematically related in any meaningful way.
Is it weird? Well, consider this example:
Say the product price is $8 per unit, and the total number of units is 31, then the total dollars would be $248, but say the TSA only reported $160. We could say, they reported for 20 units (analogous to the 560). But we WOULDN'T say they reported for 31 units because 248/31 is 5.161 which isn't even (NOT analogous to the 1170). So, a partial order in no way implies that the TSA reported number divides evenly by both. It WOULD if the partial order is simply 1/2 or 1/3 but not if it ISN'T related like 20 and 31, and like 560 and 1170 appear to be.
So, how unusual is it that the reported number divides by both? It's very unusual. I ran a program that takes a cost/price per unit of $15000, $15001, etc.. all the way up to $55000 to see how many of those that we apply to 1170 units (ie 15000 x 1170, 15001 x 1170) also divide by 560, and as you can see in this partial list, it is only 1 out of every 56 (notice that each listed increments by 56 more than the previous one). I have bolded the one that multiplies out to the $21,556,080 number reported:
unit cost/price for 1170 of 15008 that divides by 560
unit cost/price for 1170 of 15064 that divides by 560
unit cost/price for 1170 of 15120 that divides by 560
unit cost/price for 1170 of 15176 that divides by 560
unit cost/price for 1170 of 15232 that divides by 560
unit cost/price for 1170 of 15288 that divides by 560
unit cost/price for 1170 of 15344 that divides by 560
unit cost/price for 1170 of 15400 that divides by 560
unit cost/price for 1170 of 15456 that divides by 560
unit cost/price for 1170 of 15512 that divides by 560
unit cost/price for 1170 of 15568 that divides by 560
unit cost/price for 1170 of 15624 that divides by 560
unit cost/price for 1170 of 15680 that divides by 560
unit cost/price for 1170 of 15736 that divides by 560
unit cost/price for 1170 of 15792 that divides by 560
unit cost/price for 1170 of 15848 that divides by 560
unit cost/price for 1170 of 15904 that divides by 560
unit cost/price for 1170 of 15960 that divides by 560
unit cost/price for 1170 of 16016 that divides by 560
unit cost/price for 1170 of 16072 that divides by 560
unit cost/price for 1170 of 16128 that divides by 560
unit cost/price for 1170 of 16184 that divides by 560
unit cost/price for 1170 of 16240 that divides by 560
unit cost/price for 1170 of 16296 that divides by 560
unit cost/price for 1170 of 16352 that divides by 560
unit cost/price for 1170 of 16408 that divides by 560
unit cost/price for 1170 of 16464 that divides by 560
unit cost/price for 1170 of 16520 that divides by 560
unit cost/price for 1170 of 16576 that divides by 560
unit cost/price for 1170 of 16632 that divides by 560
unit cost/price for 1170 of 16688 that divides by 560
unit cost/price for 1170 of 16744 that divides by 560
unit cost/price for 1170 of 16800 that divides by 560
unit cost/price for 1170 of 16856 that divides by 560
unit cost/price for 1170 of 16912 that divides by 560
unit cost/price for 1170 of 16968 that divides by 560
unit cost/price for 1170 of 17024 that divides by 560
unit cost/price for 1170 of 17080 that divides by 560
unit cost/price for 1170 of 17136 that divides by 560
unit cost/price for 1170 of 17192 that divides by 560
unit cost/price for 1170 of 17248 that divides by 560
unit cost/price for 1170 of 17304 that divides by 560
unit cost/price for 1170 of 17360 that divides by 560
unit cost/price for 1170 of 17416 that divides by 560
unit cost/price for 1170 of 17472 that divides by 560
unit cost/price for 1170 of 17528 that divides by 560
unit cost/price for 1170 of 17584 that divides by 560
unit cost/price for 1170 of 17640 that divides by 560
unit cost/price for 1170 of 17696 that divides by 560
unit cost/price for 1170 of 17752 that divides by 560
unit cost/price for 1170 of 17808 that divides by 560
unit cost/price for 1170 of 17864 that divides by 560
unit cost/price for 1170 of 17920 that divides by 560
unit cost/price for 1170 of 17976 that divides by 560
unit cost/price for 1170 of 18032 that divides by 560
unit cost/price for 1170 of 18088 that divides by 560
unit cost/price for 1170 of 18144 that divides by 560
unit cost/price for 1170 of 18200 that divides by 560
unit cost/price for 1170 of 18256 that divides by 560
unit cost/price for 1170 of 18312 that divides by 560
unit cost/price for 1170 of 18368 that divides by 560
unit cost/price for 1170 of 18424 that divides by 560
unit cost/price for 1170 of 18480 that divides by 560
unit cost/price for 1170 of 18536 that divides by 560
unit cost/price for 1170 of 18592 that divides by 560
unit cost/price for 1170 of 18648 that divides by 560
unit cost/price for 1170 of 18704 that divides by 560
One could easily say that the total award was for $45,036,810 which was then pro-rated for the 560:
45,036,810 x 560/1170 = $21,556,080
but that in no way explains why $21,556,080 divides by 1170, when that seems very unlikely.
And for those that think maybe they reported the COST for 1170, that doesn't help explain why the COST of the whole project would be divisible by 560...only a 1 in 56 chance of that.
Because it is not at at likely to have happened this way, there seems to a real reason why it divides by both numbers, but I can't figure out what the relationship might be between 560 and 1170 that would cause it to work out this way.
Can you?
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