Gwyneth Paltrow has apparently failed at the food stamp challenge. She quit after four days, she reports on her website, GOOP. But then, most everyone who takes the challenge does it wrong.

The Hollywood A-lister tried eating for only $29 this week, the weekly amount the average food stamp recipient receives in the Supplemental Nutrition Assistance Program. Earlier this week, Paltrow tweeted a photo of her $29 grocery haul.

This is what $29 gets you at the grocery store—what families on SNAP (i.e. food stamps) have to live on for a week. pic.twitter.com/OZMPA3nxij — Gwyneth Paltrow (@GwynethPaltrow) April 9, 2015

The actress and GOOP curator has earned a reputation for ideas that range from pretentious and out of touch (see: conscious uncoupling) to downright weird (does water have feelings?). And once again, she has created a media freakout with her SNAP challenge. Time dismissed it as "poverty tourism," while Slate is telling everyone to just lay off already. No matter your take, Paltrow at the very least doesn't seem to have stretched her $29 very well. (Really, when you're eating on a budget, who prioritizes limes?)

The SNAP challenge has been around for a few years, and has become a way for high-profile Americans like Sen. Cory Booker and Panera CEO Ron Shaich to draw attention to the meager food budget many Americans live on. Usually when people take the challenge, they try to live off of the average SNAP payout of $29 per week, or around $4 per day.

The challenge might make for good publicity, but it's flawed in two big ways. One is that it gets the math on how the USDA hands out benefits entirely wrong. And because of that, it fails to capture the grim reality of being a low-income American.

How SNAP benefits are awarded

SNAP benefits are handed out on a sliding scale — someone who earns more money gets a smaller benefit, and vice versa. And those benefits help a huge number of people: more than 46.5 million received SNAP benefits last year, or around one in seven Americans.

To qualify for SNAP, a household generally has to meet two income thresholds: total income and net income (that is, total income minus deductions for things like child support, some medical expenses, and some housing costs). The SNAP formula assumes that households will spend 30 percent of their income on food, as the Center on Budget and Policy Priorities explains, but for many low-income Americans, 30 percent of income is not enough to eat. So SNAP provides households with enough extra money to meet the costs of the Thrifty Food Plan, a meal plan that the USDA has devised to be low-cost but healthful. Altogether, the USDA figures that the Thrifty Meal Plan costs around $38 for most adult females (nearly $5.50 a day) and $43 for adult men (around $6.20 a day).

So when the average person gets a little over $4 a day in benefits, the SNAP formula assumes that person has other money to spend on food. The government doesn't in fact expect people to live on $4 a day.

It's true that plenty of SNAP households are in dire straits. One in five reported no income at all in fiscal year 2012. And less than 40 percent had no net income, after subtracting out those necessities mentioned above. But those households with the fewest resources get more than the average SNAP payout — for example, the maximum allotment for a person who lives alone, according to the USDA, is $194 a month, or around $45 a week or $6.50 a day (residents of Hawaii and Alaska get slightly higher benefits).

The philosophy of SNAP

All this isn't just to make the (fairly pedantic) point that Gwyneth should really be buying her limes and tortillas on five or six dollars a day instead of four. Nor is it to say that $6 a day, as opposed to $4, is a princely sum to eat on (it's not), or that the families who are receiving $4 a day are otherwise living large (they're not). Rather, it's to say that the SNAP challenge misses the point.

For many families on SNAP, the true challenge isn't just stretching a small food budget; it's deciding which of their other dollars will go toward food versus keeping the electricity on or to staying up to date on rent. Food is just one of myriad problems.

That's not the only problem. Whether they know it or not, people who do the SNAP challenge are raising a basic question about the point of the SNAP program. If you truly want all SNAP recipients to receive enough money to eat well, without spending any outside money, that means not only upping SNAP spending but also changing the philosophy of the program, which is (as the name suggests) to supplement families' food budgets. (And if you truly think the government has a duty to meet people's basic needs, then it's not just a matter of reforming SNAP; it may simply be time for the government to provide a basic income for everyone.)

For anyone who really wants to experience SNAP's unfairness, there are other ways to do it. For example, you could drain your bank account — that's because in five states, the program has an asset limit, in addition to having income limits. At the federal level, the asset limit is set at $2,250, meaning a family that falls on hard times may not qualify for SNAP, though states can raise or eliminate it as they like. (Nebraska, however, has taken the unique step of raising the limit far higher, to $25,000.) Or you can take the old-fashioned route and just write to your legislators. It's not as sexy as tweeting your $29 grocery haul, but it at least gets the right people to listen.